LMFDB - Embedded newform 552.2.j.d.323.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(323,552)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("552.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.j (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.13
Character	$\chi$	$=$	552.323
Dual form			552.2.j.d.323.14

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.964429 - 1.03435i) q^{2} +(-0.513686 + 1.65412i) q^{3} +(-0.139754 + 1.99511i) q^{4} +2.51134 q^{5} +(2.20635 - 1.06396i) q^{6} -2.77384i q^{7} +(2.19842 - 1.77959i) q^{8} +(-2.47225 - 1.69940i) q^{9} +O(q^{10})$	\(q+(-0.964429 - 1.03435i) q^{2} +(-0.513686 + 1.65412i) q^{3} +(-0.139754 + 1.99511i) q^{4} +2.51134 q^{5} +(2.20635 - 1.06396i) q^{6} -2.77384i q^{7} +(2.19842 - 1.77959i) q^{8} +(-2.47225 - 1.69940i) q^{9} +(-2.42201 - 2.59760i) q^{10} -5.36177i q^{11} +(-3.22837 - 1.25603i) q^{12} +3.90363i q^{13} +(-2.86912 + 2.67518i) q^{14} +(-1.29004 + 4.15406i) q^{15} +(-3.96094 - 0.557650i) q^{16} -6.27537i q^{17} +(0.626542 + 4.19612i) q^{18} -0.842460 q^{19} +(-0.350970 + 5.01040i) q^{20} +(4.58828 + 1.42488i) q^{21} +(-5.54594 + 5.17105i) q^{22} +1.00000 q^{23} +(1.81436 + 4.55061i) q^{24} +1.30682 q^{25} +(4.03772 - 3.76478i) q^{26} +(4.08098 - 3.21646i) q^{27} +(5.53413 + 0.387656i) q^{28} +4.73312 q^{29} +(5.54090 - 2.67195i) q^{30} -5.16790i q^{31} +(3.24324 + 4.63480i) q^{32} +(8.86904 + 2.75427i) q^{33} +(-6.49092 + 6.05215i) q^{34} -6.96606i q^{35} +(3.73600 - 4.69492i) q^{36} -5.17881i q^{37} +(0.812493 + 0.871397i) q^{38} +(-6.45709 - 2.00524i) q^{39} +(5.52098 - 4.46915i) q^{40} +8.80915i q^{41} +(-2.95125 - 6.12008i) q^{42} +0.848253 q^{43} +(10.6973 + 0.749330i) q^{44} +(-6.20867 - 4.26777i) q^{45} +(-0.964429 - 1.03435i) q^{46} -4.84556 q^{47} +(2.95710 - 6.26543i) q^{48} -0.694215 q^{49} +(-1.26033 - 1.35171i) q^{50} +(10.3802 + 3.22357i) q^{51} +(-7.78818 - 0.545549i) q^{52} +11.2894 q^{53} +(-7.26275 - 1.11911i) q^{54} -13.4652i q^{55} +(-4.93630 - 6.09809i) q^{56} +(0.432759 - 1.39353i) q^{57} +(-4.56476 - 4.89570i) q^{58} -12.0771i q^{59} +(-8.10753 - 3.15432i) q^{60} +10.9153i q^{61} +(-5.34541 + 4.98407i) q^{62} +(-4.71387 + 6.85765i) q^{63} +(1.66613 - 7.82458i) q^{64} +9.80334i q^{65} +(-5.70469 - 11.8300i) q^{66} -1.54517 q^{67} +(12.5201 + 0.877009i) q^{68} +(-0.513686 + 1.65412i) q^{69} +(-7.20534 + 6.71827i) q^{70} +1.08766 q^{71} +(-8.45929 + 0.663596i) q^{72} -1.99252 q^{73} +(-5.35669 + 4.99459i) q^{74} +(-0.671293 + 2.16164i) q^{75} +(0.117737 - 1.68080i) q^{76} -14.8727 q^{77} +(4.15329 + 8.61280i) q^{78} +9.76669i q^{79} +(-9.94725 - 1.40045i) q^{80} +(3.22408 + 8.40270i) q^{81} +(9.11173 - 8.49580i) q^{82} -9.45161i q^{83} +(-3.48403 + 8.95500i) q^{84} -15.7596i q^{85} +(-0.818080 - 0.877389i) q^{86} +(-2.43134 + 7.82917i) q^{87} +(-9.54175 - 11.7874i) q^{88} +11.4954i q^{89} +(1.57346 + 10.5379i) q^{90} +10.8281 q^{91} +(-0.139754 + 1.99511i) q^{92} +(8.54835 + 2.65468i) q^{93} +(4.67319 + 5.01199i) q^{94} -2.11570 q^{95} +(-9.33255 + 2.98389i) q^{96} +9.24065 q^{97} +(0.669521 + 0.718060i) q^{98} +(-9.11179 + 13.2557i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) $ 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9	$ 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24} + 22 q^{25} + 11 q^{26} - 16 q^{27} + 6 q^{28} + 2 q^{30} - 20 q^{32} + 12 q^{33} + 14 q^{34} - 24 q^{36} - 22 q^{38} + 8 q^{39} + 4 q^{40} - 44 q^{42} + 28 q^{43} + 56 q^{44} - 8 q^{45} + 30 q^{48} - 50 q^{49} + 20 q^{50} + 28 q^{51} - q^{52} + 24 q^{53} + 52 q^{54} - 34 q^{56} - 8 q^{57} - 21 q^{58} - 42 q^{60} - 79 q^{62} - 16 q^{63} + 7 q^{64} - 62 q^{66} - 4 q^{67} + 20 q^{68} + 2 q^{69} - 8 q^{70} + 22 q^{72} + 4 q^{73} + 36 q^{74} - 6 q^{75} + 14 q^{76} + 32 q^{77} + 27 q^{78} - 52 q^{80} + 18 q^{81} + 11 q^{82} - 80 q^{84} - 28 q^{86} - 48 q^{87} - 38 q^{88} - 46 q^{90} - 8 q^{91} + 4 q^{92} - 22 q^{93} + q^{94} - 16 q^{95} + 9 q^{96} + 20 q^{97} + 64 q^{98}+O(q^{100}) $ 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * q^96 + 20 * q^97 + 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.964429	−	1.03435i	−0.681954	−	0.731395i
$2$	−0.964429	−	1.03435i	−0.681954	−	0.731395i
$3$	−0.513686	+	1.65412i	−0.296576	+	0.955009i
$3$	−0.513686	+	1.65412i	−0.296576	+	0.955009i
$4$	−0.139754	+	1.99511i	−0.0698770	+	0.997556i
$5$	2.51134			1.12310			0.561552	−	0.827441i	$-0.310204\pi$
$5$	2.51134			1.12310			0.561552	+	0.827441i	$0.310204\pi$
$6$	2.20635	−	1.06396i	0.900740	−	0.434358i
$7$		−	2.77384i		−	1.04841i	−0.851591	−	0.524207i	$-0.824362\pi$
$7$		−	2.77384i		−	1.04841i	0.851591	−	0.524207i	$-0.175638\pi$
$8$	2.19842	−	1.77959i	0.777260	−	0.629179i
$9$	−2.47225	−	1.69940i	−0.824085	−	0.566466i
$10$	−2.42201	−	2.59760i	−0.765906	−	0.821433i
$11$		−	5.36177i		−	1.61664i	−0.588746	−	0.808318i	$-0.700378\pi$
$11$		−	5.36177i		−	1.61664i	0.588746	−	0.808318i	$-0.299622\pi$
$12$	−3.22837	−	1.25603i	−0.931951	−	0.362585i
$13$			3.90363i			1.08267i	0.840806	+	0.541336i	$0.182081\pi$
$13$			3.90363i			1.08267i	−0.840806	+	0.541336i	$0.817919\pi$
$14$	−2.86912	+	2.67518i	−0.766805	+	0.714971i
$15$	−1.29004	+	4.15406i	−0.333086	+	1.07257i
$16$	−3.96094	−	0.557650i	−0.990234	−	0.139412i
$17$		−	6.27537i		−	1.52200i	−0.648751	−	0.761000i	$-0.724708\pi$
$17$		−	6.27537i		−	1.52200i	0.648751	−	0.761000i	$-0.275292\pi$
$18$	0.626542	+	4.19612i	0.147677	+	0.989036i
$19$	−0.842460			−0.193274			−0.0966368	−	0.995320i	$-0.530809\pi$
$19$	−0.842460			−0.193274			−0.0966368	+	0.995320i	$0.530809\pi$
$20$	−0.350970	+	5.01040i	−0.0784792	+	1.12036i
$21$	4.58828	+	1.42488i	1.00125	+	0.310935i
$22$	−5.54594	+	5.17105i	−1.18240	+	1.10247i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	1.81436	+	4.55061i	0.370355	+	0.928890i
$25$	1.30682			0.261364
$26$	4.03772	−	3.76478i	0.791861	−	0.738333i
$27$	4.08098	−	3.21646i	0.785385	−	0.619008i
$28$	5.53413	+	0.387656i	1.04585	+	0.0732601i
$29$	4.73312			0.878919			0.439459	−	0.898262i	$-0.355170\pi$
$29$	4.73312			0.878919			0.439459	+	0.898262i	$0.355170\pi$
$30$	5.54090	−	2.67195i	1.01163	−	0.487829i
$31$		−	5.16790i		−	0.928183i	−0.885787	−	0.464091i	$-0.846381\pi$
$31$		−	5.16790i		−	0.928183i	0.885787	−	0.464091i	$-0.153619\pi$
$32$	3.24324	+	4.63480i	0.573329	+	0.819325i
$33$	8.86904	+	2.75427i	1.54390	+	0.479456i
$34$	−6.49092	+	6.05215i	−1.11318	+	1.03793i
$35$		−	6.96606i		−	1.17748i
$36$	3.73600	−	4.69492i	0.622666	−	0.782487i
$37$		−	5.17881i		−	0.851391i	−0.904867	−	0.425695i	$-0.860030\pi$
$37$		−	5.17881i		−	0.851391i	0.904867	−	0.425695i	$-0.139970\pi$
$38$	0.812493	+	0.871397i	0.131804	+	0.141359i
$39$	−6.45709	−	2.00524i	−1.03396	−	0.321095i
$40$	5.52098	−	4.46915i	0.872944	−	0.706634i
$41$			8.80915i			1.37576i	0.725825	+	0.687879i	$0.241458\pi$
$41$			8.80915i			1.37576i	−0.725825	+	0.687879i	$0.758542\pi$
$42$	−2.95125	−	6.12008i	−0.455387	−	0.944350i
$43$	0.848253			0.129357			0.0646787	−	0.997906i	$-0.479398\pi$
$43$	0.848253			0.129357			0.0646787	+	0.997906i	$0.479398\pi$
$44$	10.6973	+	0.749330i	1.61268	+	0.112966i
$45$	−6.20867	−	4.26777i	−0.925533	−	0.636201i
$46$	−0.964429	−	1.03435i	−0.142197	−	0.152506i
$47$	−4.84556			−0.706797			−0.353399	−	0.935473i	$-0.614974\pi$
$47$	−4.84556			−0.706797			−0.353399	+	0.935473i	$0.614974\pi$
$48$	2.95710	−	6.26543i	0.426820	−	0.904336i
$49$	−0.694215			−0.0991736
$50$	−1.26033	−	1.35171i	−0.178238	−	0.191160i
$51$	10.3802	+	3.22357i	1.45352	+	0.451390i
$52$	−7.78818	−	0.545549i	−1.08003	−	0.0756540i
$53$	11.2894			1.55071			0.775357	−	0.631523i	$-0.217570\pi$
$53$	11.2894			1.55071			0.775357	+	0.631523i	$0.217570\pi$
$54$	−7.26275	−	1.11911i	−0.988336	−	0.152291i
$55$		−	13.4652i		−	1.81565i
$56$	−4.93630	−	6.09809i	−0.659641	−	0.814891i
$57$	0.432759	−	1.39353i	0.0573204	−	0.184578i
$58$	−4.56476	−	4.89570i	−0.599382	−	0.642837i
$59$		−	12.0771i		−	1.57230i	−0.618033	−	0.786152i	$-0.712070\pi$
$59$		−	12.0771i		−	1.57230i	0.618033	−	0.786152i	$-0.287930\pi$
$60$	−8.10753	−	3.15432i	−1.04668	−	0.407221i
$61$			10.9153i			1.39756i	0.715336	+	0.698781i	$0.246274\pi$
$61$			10.9153i			1.39756i	−0.715336	+	0.698781i	$0.753726\pi$
$62$	−5.34541	+	4.98407i	−0.678868	+	0.632978i
$63$	−4.71387	+	6.85765i	−0.593892	+	0.863983i
$64$	1.66613	−	7.82458i	0.208266	−	0.978072i
$65$			9.80334i			1.21595i
$66$	−5.70469	−	11.8300i	−0.702198	−	1.45617i
$67$	−1.54517			−0.188772			−0.0943861	−	0.995536i	$-0.530089\pi$
$67$	−1.54517			−0.188772			−0.0943861	+	0.995536i	$0.530089\pi$
$68$	12.5201	+	0.877009i	1.51828	+	0.106353i
$69$	−0.513686	+	1.65412i	−0.0618405	+	0.199133i
$70$	−7.20534	+	6.71827i	−0.861202	+	0.802987i
$71$	1.08766			0.129081			0.0645405	−	0.997915i	$-0.479442\pi$
$71$	1.08766			0.129081			0.0645405	+	0.997915i	$0.479442\pi$
$72$	−8.45929	+	0.663596i	−0.996937	+	0.0782055i
$73$	−1.99252			−0.233206			−0.116603	−	0.993179i	$-0.537201\pi$
$73$	−1.99252			−0.233206			−0.116603	+	0.993179i	$0.537201\pi$
$74$	−5.35669	+	4.99459i	−0.622703	+	0.580609i
$75$	−0.671293	+	2.16164i	−0.0775143	+	0.249605i
$76$	0.117737	−	1.68080i	0.0135054	−	0.192801i
$77$	−14.8727			−1.69490
$78$	4.15329	+	8.61280i	0.470268	+	0.975207i
$79$			9.76669i			1.09884i	0.835547	+	0.549419i	$0.185151\pi$
$79$			9.76669i			1.09884i	−0.835547	+	0.549419i	$0.814849\pi$
$80$	−9.94725	−	1.40045i	−1.11214	−	0.156575i
$81$	3.22408	+	8.40270i	0.358232	+	0.933633i
$82$	9.11173	−	8.49580i	1.00622	−	0.938204i
$83$		−	9.45161i		−	1.03745i	−0.854942	−	0.518724i	$-0.826407\pi$
$83$		−	9.45161i		−	1.03745i	0.854942	−	0.518724i	$-0.173593\pi$
$84$	−3.48403	+	8.95500i	−0.380139	+	0.977071i
$85$		−	15.7596i		−	1.70937i
$86$	−0.818080	−	0.877389i	−0.0882158	−	0.0946113i
$87$	−2.43134	+	7.82917i	−0.260667	+	0.839375i
$88$	−9.54175	−	11.7874i	−1.01715	−	1.25655i
$89$			11.4954i			1.21851i	0.792975	+	0.609254i	$0.208531\pi$
$89$			11.4954i			1.21851i	−0.792975	+	0.609254i	$0.791469\pi$
$90$	1.57346	+	10.5379i	0.165857	+	1.11079i
$91$	10.8281			1.13509
$92$	−0.139754	+	1.99511i	−0.0145704	+	0.208005i
$93$	8.54835	+	2.65468i	0.886423	+	0.275277i
$94$	4.67319	+	5.01199i	0.482003	+	0.516948i
$95$	−2.11570			−0.217066
$96$	−9.33255	+	2.98389i	−0.952499	+	0.304542i
$97$	9.24065			0.938246			0.469123	−	0.883133i	$-0.344570\pi$
$97$	9.24065			0.938246			0.469123	+	0.883133i	$0.344570\pi$
$98$	0.669521	+	0.718060i	0.0676318	+	0.0725351i
$99$	−9.11179	+	13.2557i	−0.915770	+	1.33224i
$100$	−0.182633	+	2.60725i	−0.0182633	+	0.260725i
$101$	4.79559			0.477180			0.238590	−	0.971120i	$-0.423315\pi$
$101$	4.79559			0.477180			0.238590	+	0.971120i	$0.423315\pi$
$102$	−6.67671	−	13.8457i	−0.661093	−	1.37093i
$103$			12.5351i			1.23512i	0.786525	+	0.617559i	$0.211878\pi$
$103$			12.5351i			1.23512i	−0.786525	+	0.617559i	$0.788122\pi$
$104$	6.94686	+	8.58184i	0.681196	+	0.841518i
$105$	11.5227	+	3.57836i	1.12450	+	0.349213i
$106$	−10.8878	−	11.6771i	−1.05752	−	1.13418i
$107$			2.48291i			0.240032i	0.992772	+	0.120016i	$0.0382945\pi$
$107$			2.48291i			0.240032i	−0.992772	+	0.120016i	$0.961705\pi$
$108$	5.84686	+	8.59152i	0.562614	+	0.826719i
$109$		−	10.9167i		−	1.04563i	−0.852446	−	0.522815i	$-0.824882\pi$
$109$		−	10.9167i		−	1.04563i	0.852446	−	0.522815i	$-0.175118\pi$
$110$	−13.9277	+	12.9863i	−1.32796	+	1.23819i
$111$	8.56639	+	2.66028i	0.813086	+	0.252502i
$112$	−1.54683	+	10.9870i	−0.146162	+	1.03818i
$113$		−	17.9096i		−	1.68480i	−0.538856	−	0.842398i	$-0.681143\pi$
$113$		−	17.9096i		−	1.68480i	0.538856	−	0.842398i	$-0.318857\pi$
$114$	−1.85876	+	0.896340i	−0.174089	+	0.0839499i
$115$	2.51134			0.234183
$116$	−0.661473	+	9.44311i	−0.0614162	+	0.876770i
$117$	6.63383	−	9.65077i	0.613298	−	0.892214i
$118$	−12.4919	+	11.6475i	−1.14997	+	1.07224i
$119$	−17.4069			−1.59569
$120$	4.55648	+	11.4281i	0.415947	+	1.04324i
$121$	−17.7486			−1.61351
$122$	11.2902	−	10.5270i	1.02217	−	0.953073i
$123$	−14.5714	−	4.52513i	−1.31386	−	0.408018i
$124$	10.3105	+	0.722236i	0.925914	+	0.0648587i
$125$	−9.27483			−0.829566
$126$	11.6394	−	1.73793i	1.03692	−	0.154827i
$127$		−	2.16694i		−	0.192285i	−0.995368	−	0.0961423i	$-0.969350\pi$
$127$		−	2.16694i		−	0.192285i	0.995368	−	0.0961423i	$-0.0306504\pi$
$128$	−9.70021	+	5.82289i	−0.857385	+	0.514675i
$129$	−0.435735	+	1.40312i	−0.0383643	+	0.123537i
$130$	10.1401	−	9.45462i	0.889343	−	0.829225i
$131$			19.6283i			1.71493i	0.514541	+	0.857466i	$0.327962\pi$
$131$			19.6283i			1.71493i	−0.514541	+	0.857466i	$0.672038\pi$
$132$	−6.73455	+	17.3098i	−0.586167	+	1.50662i
$133$			2.33685i			0.202631i
$134$	1.49020	+	1.59824i	0.128734	+	0.138067i
$135$	10.2487	−	8.07762i	0.882069	−	0.695210i
$136$	−11.1676	−	13.7959i	−0.957612	−	1.18299i
$137$		−	3.18575i		−	0.272177i	−0.990697	−	0.136089i	$-0.956547\pi$
$137$		−	3.18575i		−	0.272177i	0.990697	−	0.136089i	$-0.0434532\pi$
$138$	2.20635	−	1.06396i	0.187817	−	0.0905699i
$139$	8.02500			0.680671			0.340336	−	0.940304i	$-0.389459\pi$
$139$	8.02500			0.680671			0.340336	+	0.940304i	$0.389459\pi$
$140$	13.8981	+	0.973536i	1.17460	+	0.0822788i
$141$	2.48909	−	8.01515i	0.209619	−	0.674998i
$142$	−1.04897	−	1.12502i	−0.0880273	−	0.0944092i
$143$	20.9304			1.75029
$144$	8.84478	+	8.10987i	0.737065	+	0.675822i
$145$	11.8865			0.987118
$146$	1.92164	+	2.06096i	0.159036	+	0.170566i
$147$	0.356608	−	1.14832i	0.0294126	−	0.0947117i
$148$	10.3323	+	0.723759i	0.849310	+	0.0594927i
$149$	4.37107			0.358092			0.179046	−	0.983841i	$-0.442699\pi$
$149$	4.37107			0.358092			0.179046	+	0.983841i	$0.442699\pi$
$150$	2.88330	−	1.39040i	0.235421	−	0.113525i
$151$			1.91587i			0.155911i	0.996957	+	0.0779555i	$0.0248392\pi$
$151$			1.91587i			0.155911i	−0.996957	+	0.0779555i	$0.975161\pi$
$152$	−1.85208	+	1.49923i	−0.150224	+	0.121604i
$153$	−10.6644	+	15.5143i	−0.862162	+	1.25426i
$154$	14.3437	+	15.3836i	1.15585	+	1.23964i
$155$		−	12.9784i		−	1.04245i
$156$	4.90308	−	12.6024i	0.392561	−	1.00900i
$157$			11.7894i			0.940897i	0.882427	+	0.470448i	$0.155908\pi$
$157$			11.7894i			0.940897i	−0.882427	+	0.470448i	$0.844092\pi$
$158$	10.1022	−	9.41928i	0.803685	−	0.749358i
$159$	−5.79918	+	18.6740i	−0.459905	+	1.48095i
$160$	8.14487	+	11.6396i	0.643908	+	0.920188i
$161$		−	2.77384i		−	0.218610i
$162$	5.58192	−	11.4386i	0.438557	−	0.898703i
$163$	2.76270			0.216391			0.108196	−	0.994130i	$-0.465493\pi$
$163$	2.76270			0.216391			0.108196	+	0.994130i	$0.465493\pi$
$164$	−17.5752	−	1.23111i	−1.37240	−	0.0961339i
$165$	22.2732	+	6.91689i	1.73396	+	0.538479i
$166$	−9.77625	+	9.11540i	−0.758785	+	0.707492i
$167$	−15.5735			−1.20511			−0.602557	−	0.798076i	$-0.705851\pi$
$167$	−15.5735			−1.20511			−0.602557	+	0.798076i	$0.705851\pi$
$168$	12.6227	−	5.03276i	0.973862	−	0.388286i
$169$	−2.23835			−0.172181
$170$	−16.3009	+	15.1990i	−1.25022	+	1.16571i
$171$	2.08277	+	1.43168i	0.159274	+	0.109483i
$172$	−0.118547	+	1.69236i	−0.00903911	+	0.129041i
$173$	−15.3241			−1.16507			−0.582535	−	0.812806i	$-0.697939\pi$
$173$	−15.3241			−1.16507			−0.582535	+	0.812806i	$0.697939\pi$
$174$	10.4429	−	5.03583i	0.791678	−	0.381765i
$175$		−	3.62491i		−	0.274017i
$176$	−2.98999	+	21.2377i	−0.225379	+	1.60085i
$177$	19.9770	+	6.20383i	1.50156	+	0.466308i
$178$	11.8902	−	11.0865i	0.891210	−	0.830966i
$179$			10.5698i			0.790021i	0.918677	+	0.395011i	$0.129259\pi$
$179$			10.5698i			0.790021i	−0.918677	+	0.395011i	$0.870741\pi$
$180$	9.38235	−	11.7905i	0.699319	−	0.878815i
$181$			12.4081i			0.922289i	0.887325	+	0.461145i	$0.152561\pi$
$181$			12.4081i			0.922289i	−0.887325	+	0.461145i	$0.847439\pi$
$182$	−10.4429	−	11.2000i	−0.774080	−	0.830199i
$183$	−18.0553	−	5.60704i	−1.33468	−	0.414484i
$184$	2.19842	−	1.77959i	0.162070	−	0.131193i
$185$		−	13.0057i		−	0.956201i
$186$	−5.49842	−	11.4022i	−0.403164	−	0.836052i
$187$	−33.6471			−2.46052
$188$	0.677186	−	9.66742i	0.0493889	−	0.705069i
$189$	−8.92196	−	11.3200i	−0.648977	−	0.823409i
$190$	2.04044	+	2.18837i	0.148029	+	0.158761i
$191$	−11.0504			−0.799575			−0.399788	−	0.916608i	$-0.630916\pi$
$191$	−11.0504			−0.799575			−0.399788	+	0.916608i	$0.630916\pi$
$192$	12.0870	+	6.77536i	0.872301	+	0.488969i
$193$	−25.3585			−1.82535			−0.912673	−	0.408691i	$-0.865985\pi$
$193$	−25.3585			−1.82535			−0.912673	+	0.408691i	$0.865985\pi$
$194$	−8.91195	−	9.55806i	−0.639841	−	0.686229i
$195$	−16.2159	−	5.03583i	−1.16125	−	0.360624i
$196$	0.0970194	−	1.38504i	0.00692996	−	0.0989312i
$197$	−9.46165			−0.674115			−0.337057	−	0.941484i	$-0.609432\pi$
$197$	−9.46165			−0.674115			−0.337057	+	0.941484i	$0.609432\pi$
$198$	22.4987	−	3.35938i	1.59891	−	0.238741i
$199$			1.84306i			0.130651i	0.997864	+	0.0653256i	$0.0208086\pi$
$199$			1.84306i			0.130651i	−0.997864	+	0.0653256i	$0.979191\pi$
$200$	2.87294	−	2.32560i	0.203147	−	0.164445i
$201$	0.793730	−	2.55590i	0.0559854	−	0.180279i
$202$	−4.62501	−	4.96032i	−0.325415	−	0.349007i
$203$		−	13.1289i		−	0.921471i
$204$	−7.88206	+	20.2592i	−0.551854	+	1.41843i
$205$			22.1228i			1.54512i
$206$	12.9656	−	12.0892i	0.903359	−	0.842294i
$207$	−2.47225	−	1.69940i	−0.171834	−	0.118116i
$208$	2.17686	−	15.4620i	0.150938	−	1.07210i
$209$			4.51708i			0.312453i
$210$	−7.41158	−	15.3696i	−0.511447	−	1.06060i
$211$	14.3130			0.985346			0.492673	−	0.870214i	$-0.336020\pi$
$211$	14.3130			0.985346			0.492673	+	0.870214i	$0.336020\pi$
$212$	−1.57774	+	22.5235i	−0.108359	+	1.54692i
$213$	−0.558713	+	1.79912i	−0.0382824	+	0.123274i
$214$	2.56819	−	2.39459i	0.175558	−	0.163691i
$215$	2.13025			0.145282
$216$	3.24775	−	14.3336i	0.220981	−	0.975278i
$217$	−14.3350			−0.973121
$218$	−11.2917	+	10.5284i	−0.764769	+	0.713072i
$219$	1.02353	−	3.29587i	0.0691635	−	0.222714i
$220$	26.8646	+	1.88182i	1.81121	+	0.126872i
$221$	24.4967			1.64783
$222$	−5.51002	−	11.4263i	−0.369808	−	0.766882i
$223$			8.87393i			0.594243i	0.954840	+	0.297121i	$0.0960266\pi$
$223$			8.87393i			0.594243i	−0.954840	+	0.297121i	$0.903973\pi$
$224$	12.8562	−	8.99624i	0.858993	−	0.601086i
$225$	−3.23079	−	2.22081i	−0.215386	−	0.148054i
$226$	−18.5248	+	17.2726i	−1.23225	+	1.14895i
$227$		−	19.3606i		−	1.28501i	−0.766282	−	0.642504i	$-0.777896\pi$
$227$		−	19.3606i		−	1.28501i	0.766282	−	0.642504i	$-0.222104\pi$
$228$	2.71977	+	1.05816i	0.180121	+	0.0700780i
$229$			0.215711i			0.0142546i	0.999975	+	0.00712729i	$0.00226871\pi$
$229$			0.215711i			0.0142546i	−0.999975	+	0.00712729i	$0.997731\pi$
$230$	−2.42201	−	2.59760i	−0.159702	−	0.171281i
$231$	7.63990	−	24.6013i	0.502669	−	1.61865i
$232$	10.4054	−	8.42301i	0.683148	−	0.552998i
$233$		−	21.7514i		−	1.42498i	−0.701683	−	0.712489i	$-0.747568\pi$
$233$		−	21.7514i		−	1.42498i	0.701683	−	0.712489i	$-0.252432\pi$
$234$	−16.3801	+	2.44579i	−1.07080	+	0.159886i
$235$	−12.1688			−0.793807
$236$	24.0951	+	1.68782i	1.56846	+	0.109868i
$237$	−16.1553	−	5.01701i	−1.04940	−	0.325890i
$238$	16.7877	+	18.0048i	1.08819	+	1.16708i
$239$	−16.1021			−1.04156			−0.520780	−	0.853691i	$-0.674359\pi$
$239$	−16.1021			−1.04156			−0.520780	+	0.853691i	$0.674359\pi$
$240$	7.42627	−	15.7346i	0.479364	−	1.01566i
$241$	−16.2558			−1.04713			−0.523563	−	0.851987i	$-0.675397\pi$
$241$	−16.2558			−1.04713			−0.523563	+	0.851987i	$0.675397\pi$
$242$	17.1173	+	18.3583i	1.10034	+	1.18011i
$243$	−15.5553	+	1.01669i	−0.997871	+	0.0652209i
$244$	−21.7773	−	1.52546i	−1.39415	−	0.0976575i
$245$	−1.74341			−0.111382
$246$	9.37254	+	19.4361i	0.597572	+	1.23920i
$247$		−	3.28865i		−	0.209252i
$248$	−9.19674	−	11.3612i	−0.583994	−	0.721439i
$249$	15.6341	+	4.85515i	0.990773	+	0.307683i
$250$	8.94491	+	9.59341i	0.565726	+	0.606740i
$251$			25.8667i			1.63269i	0.577563	+	0.816346i	$0.304004\pi$
$251$			25.8667i			1.63269i	−0.577563	+	0.816346i	$0.695996\pi$
$252$	−13.0230	−	10.3631i	−0.820371	−	0.652813i
$253$		−	5.36177i		−	0.337092i
$254$	−2.24137	+	2.08986i	−0.140636	+	0.131129i
$255$	26.0683	+	8.09547i	1.63246	+	0.506958i
$256$	15.3781	+	4.41763i	0.961128	+	0.276102i
$257$		−	8.67089i		−	0.540876i	−0.962737	−	0.270438i	$-0.912832\pi$
$257$		−	8.67089i		−	0.540876i	0.962737	−	0.270438i	$-0.0871684\pi$
$258$	1.87155	−	0.902503i	0.116517	−	0.0561874i
$259$	−14.3652			−0.892611
$260$	−19.5588	−	1.37006i	−1.21298	−	0.0849673i
$261$	−11.7015	−	8.04347i	−0.724304	−	0.497878i
$262$	20.3025	−	18.9301i	1.25429	−	1.16950i
$263$	24.5405			1.51323			0.756615	−	0.653860i	$-0.226852\pi$
$263$	24.5405			1.51323			0.756615	+	0.653860i	$0.226852\pi$
$264$	24.3994	−	9.72820i	1.50168	−	0.598729i
$265$	28.3514			1.74161
$266$	2.41712	−	2.25373i	0.148203	−	0.138185i
$267$	−19.0148	−	5.90501i	−1.16369	−	0.361381i
$268$	0.215943	−	3.08278i	0.0131908	−	0.188311i
$269$	18.0778			1.10222			0.551111	−	0.834432i	$-0.314204\pi$
$269$	18.0778			1.10222			0.551111	+	0.834432i	$0.314204\pi$
$270$	−18.2392	−	2.81046i	−1.11000	−	0.171039i
$271$			2.29321i			0.139302i	0.997571	+	0.0696512i	$0.0221886\pi$
$271$			2.29321i			0.139302i	−0.997571	+	0.0696512i	$0.977811\pi$
$272$	−3.49946	+	24.8564i	−0.212186	+	1.50714i
$273$	−5.56222	+	17.9110i	−0.336641	+	1.08402i
$274$	−3.29518	+	3.07243i	−0.199069	+	0.185612i
$275$		−	7.00686i		−	0.422530i
$276$	−3.22837	−	1.25603i	−0.194325	−	0.0756041i
$277$		−	22.9556i		−	1.37927i	−0.724157	−	0.689635i	$-0.757771\pi$
$277$		−	22.9556i		−	1.37927i	0.724157	−	0.689635i	$-0.242229\pi$
$278$	−7.73954	−	8.30065i	−0.464187	−	0.497840i
$279$	−8.78233	+	12.7764i	−0.525784	+	0.764901i
$280$	−12.3967	−	15.3144i	−0.740846	−	0.915208i
$281$		−	1.26945i		−	0.0757293i	−0.999283	−	0.0378647i	$-0.987944\pi$
$281$		−	1.26945i		−	0.0757293i	0.999283	−	0.0378647i	$-0.0120556\pi$
$282$	−10.6910	+	5.15546i	−0.636641	+	0.307003i
$283$	−0.00124766			−7.41659e−5			−3.70829e−5	−	1.00000i	$-0.500012\pi$
$283$	−0.00124766			−7.41659e−5			−3.70829e−5		1.00000i	$0.500012\pi$
$284$	−0.152004	+	2.16999i	−0.00901980	+	0.128765i
$285$	1.08681	−	3.49963i	0.0643768	−	0.207300i
$286$	−20.1859	−	21.6493i	−1.19362	−	1.28015i
$287$	24.4352			1.44237
$288$	−0.141727	−	16.9700i	−0.00835133	−	0.999965i
$289$	−22.3803			−1.31649
$290$	−11.4637	−	12.2948i	−0.673169	−	0.721973i
$291$	−4.74679	+	15.2852i	−0.278262	+	0.896034i
$292$	0.278462	−	3.97529i	0.0162958	−	0.232636i
$293$	11.8156			0.690274			0.345137	−	0.938552i	$-0.387832\pi$
$293$	11.8156			0.690274			0.345137	+	0.938552i	$0.387832\pi$
$294$	−1.53168	+	0.738614i	−0.0893296	+	0.0430768i
$295$		−	30.3297i		−	1.76586i
$296$	−9.21615	−	11.3852i	−0.535678	−	0.661752i
$297$	−17.2459	−	21.8813i	−1.00071	−	1.26968i
$298$	−4.21559	−	4.52121i	−0.244203	−	0.261907i
$299$			3.90363i			0.225753i
$300$	−4.21889	−	1.64140i	−0.243578	−	0.0947664i
$301$		−	2.35292i		−	0.135620i
$302$	1.98167	−	1.84772i	0.114032	−	0.106324i
$303$	−2.46343	+	7.93251i	−0.141520	+	0.455711i
$304$	3.33693	+	0.469798i	0.191386	+	0.0269447i
$305$			27.4120i			1.56961i
$306$	26.3322	−	3.93178i	1.50531	−	0.224765i
$307$	7.09717			0.405057			0.202529	−	0.979276i	$-0.435084\pi$
$307$	7.09717			0.405057			0.202529	+	0.979276i	$0.435084\pi$
$308$	2.07852	−	29.6727i	0.118435	−	1.69076i
$309$	−20.7346	−	6.43909i	−1.17955	−	0.366307i
$310$	−13.4241	+	12.5167i	−0.762440	+	0.710901i
$311$	−23.6876			−1.34320			−0.671601	−	0.740913i	$-0.734393\pi$
$311$	−23.6876			−1.34320			−0.671601	+	0.740913i	$0.734393\pi$
$312$	−17.7639	+	7.08260i	−1.00568	+	0.400973i
$313$	28.0187			1.58371			0.791856	−	0.610708i	$-0.209115\pi$
$313$	28.0187			1.58371			0.791856	+	0.610708i	$0.209115\pi$
$314$	12.1944	−	11.3700i	0.688167	−	0.641649i
$315$	−11.8381	+	17.2219i	−0.667003	+	0.970343i
$316$	−19.4856	−	1.36494i	−1.09615	−	0.0767836i
$317$	30.8136			1.73066			0.865332	−	0.501200i	$-0.167108\pi$
$317$	30.8136			1.73066			0.865332	+	0.501200i	$0.167108\pi$
$318$	24.9083	−	12.0114i	1.39679	−	0.673565i
$319$		−	25.3779i		−	1.42089i
$320$	4.18422	−	19.6502i	0.233905	−	1.09848i
$321$	−4.10704	−	1.27543i	−0.229232	−	0.0711877i
$322$	−2.86912	+	2.67518i	−0.159890	+	0.149082i
$323$			5.28675i			0.294162i
$324$	−17.2149	+	5.25809i	−0.956383	+	0.292116i
$325$			5.10134i			0.282971i
$326$	−2.66443	−	2.85759i	−0.147569	−	0.158267i
$327$	18.0576	+	5.60775i	0.998587	+	0.310109i
$328$	15.6767	+	19.3662i	0.865599	+	1.06932i
$329$			13.4408i			0.741016i
$330$	−14.3264	−	29.7091i	−0.788642	−	1.63543i
$331$	30.1143			1.65523			0.827616	−	0.561294i	$-0.189696\pi$
$331$	30.1143			1.65523			0.827616	+	0.561294i	$0.189696\pi$
$332$	18.8570	+	1.32090i	1.03491	+	0.0724938i
$333$	−8.80086	+	12.8033i	−0.482284	+	0.701618i
$334$	15.0195	+	16.1084i	0.821832	+	0.881414i
$335$	−3.88043			−0.212011
$336$	−17.3793	−	8.20253i	−0.948120	−	0.447485i
$337$	1.83553			0.0999879			0.0499939	−	0.998750i	$-0.484080\pi$
$337$	1.83553			0.0999879			0.0499939	+	0.998750i	$0.484080\pi$
$338$	2.15873	+	2.31523i	0.117419	+	0.125932i
$339$	29.6248	+	9.19992i	1.60900	+	0.499671i
$340$	31.4421	+	2.20246i	1.70519	+	0.119445i
$341$	−27.7091			−1.50053
$342$	−0.527837	−	3.53506i	−0.0285421	−	0.191154i
$343$		−	17.4913i		−	0.944440i
$344$	1.86482	−	1.50954i	0.100544	−	0.0813890i
$345$	−1.29004	+	4.15406i	−0.0694533	+	0.223647i
$346$	14.7790	+	15.8505i	0.794524	+	0.852126i
$347$			4.44029i			0.238367i	0.992872	+	0.119184i	$0.0380277\pi$
$347$			4.44029i			0.238367i	−0.992872	+	0.119184i	$0.961972\pi$
$348$	−15.2803	−	5.94495i	−0.819109	−	0.318683i
$349$			33.5648i			1.79668i	0.439299	+	0.898341i	$0.355227\pi$
$349$			33.5648i			1.79668i	−0.439299	+	0.898341i	$0.644773\pi$
$350$	−3.74942	+	3.49597i	−0.200415	+	0.186867i
$351$	12.5559	+	15.9306i	0.670183	+	0.850315i
$352$	24.8508	−	17.3895i	1.32455	−	0.926864i
$353$		−	11.4363i		−	0.608693i	−0.952561	−	0.304346i	$-0.901562\pi$
$353$		−	11.4363i		−	0.608693i	0.952561	−	0.304346i	$-0.0984380\pi$
$354$	−12.8495	−	26.6463i	−0.682943	−	1.41624i
$355$	2.73147			0.144971
$356$	−22.9346	−	1.60653i	−1.21553	−	0.0851457i
$357$	8.94167	−	28.7932i	0.473244	−	1.52390i
$358$	10.9328	−	10.1938i	0.577817	−	0.538758i
$359$	15.2222			0.803398			0.401699	−	0.915772i	$-0.368420\pi$
$359$	15.2222			0.803398			0.401699	+	0.915772i	$0.368420\pi$
$360$	−21.2441	+	1.66651i	−1.11966	+	0.0878330i
$361$	−18.2903			−0.962645
$362$	12.8343	−	11.9668i	0.674558	−	0.628959i
$363$	9.11721	−	29.3584i	0.478529	−	1.54092i
$364$	−1.51327	+	21.6032i	−0.0793168	+	1.13232i
$365$	−5.00388			−0.261915
$366$	11.6134	+	24.0830i	0.607042	+	1.25884i
$367$			11.3908i			0.594593i	0.954785	+	0.297296i	$0.0960850\pi$
$367$			11.3908i			0.594593i	−0.954785	+	0.297296i	$0.903915\pi$
$368$	−3.96094	−	0.557650i	−0.206478	−	0.0290695i
$369$	14.9703	−	21.7785i	0.779321	−	1.13374i
$370$	−13.4525	+	12.5431i	−0.699360	+	0.652085i
$371$		−	31.3150i		−	1.62579i
$372$	−6.49104	+	16.6839i	−0.336545	+	0.865021i
$373$			25.0856i			1.29889i	0.760411	+	0.649443i	$0.224998\pi$
$373$			25.0856i			1.29889i	−0.760411	+	0.649443i	$0.775002\pi$
$374$	32.4502	+	34.8028i	1.67796	+	1.79961i
$375$	4.76434	−	15.3417i	0.246030	−	0.792243i
$376$	−10.6526	+	8.62310i	−0.549365	+	0.444702i
$377$			18.4764i			0.951582i
$378$	−3.10423	+	20.1458i	−0.159665	+	1.03619i
$379$	6.98660			0.358877			0.179439	−	0.983769i	$-0.442572\pi$
$379$	6.98660			0.358877			0.179439	+	0.983769i	$0.442572\pi$
$380$	0.295678	−	4.22106i	0.0151680	−	0.216536i
$381$	3.58438	+	1.11312i	0.183634	+	0.0570271i
$382$	10.6573	+	11.4299i	0.545274	+	0.584805i
$383$	26.2784			1.34276			0.671382	−	0.741111i	$-0.265701\pi$
$383$	26.2784			1.34276			0.671382	+	0.741111i	$0.265701\pi$
$384$	−4.64893	−	19.0365i	−0.237239	−	0.971451i
$385$	−37.3504			−1.90355
$386$	24.4565	+	26.2295i	1.24480	+	1.33505i
$387$	−2.09710	−	1.44152i	−0.106601	−	0.0732766i
$388$	−1.29142	+	18.4361i	−0.0655619	+	0.935953i
$389$	5.49437			0.278576			0.139288	−	0.990252i	$-0.455519\pi$
$389$	5.49437			0.278576			0.139288	+	0.990252i	$0.455519\pi$
$390$	10.4303	+	21.6296i	0.528160	+	1.09526i
$391$		−	6.27537i		−	0.317359i
$392$	−1.52618	+	1.23542i	−0.0770837	+	0.0623980i
$393$	−32.4676	−	10.0828i	−1.63777	−	0.508608i
$394$	9.12509	+	9.78665i	0.459715	+	0.493044i
$395$			24.5275i			1.23411i
$396$	−25.1731	−	20.0316i	−1.26500	−	1.00662i
$397$		−	24.8119i		−	1.24527i	−0.782511	−	0.622636i	$-0.786062\pi$
$397$		−	24.8119i		−	1.24527i	0.782511	−	0.622636i	$-0.213938\pi$
$398$	1.90637	−	1.77750i	0.0955576	−	0.0890981i
$399$	−3.86544	−	1.20041i	−0.193514	−	0.0600955i
$400$	−5.17622	−	0.728747i	−0.258811	−	0.0364373i
$401$		−	15.4431i		−	0.771193i	−0.922668	−	0.385596i	$-0.873996\pi$
$401$		−	15.4431i		−	0.771193i	0.922668	−	0.385596i	$-0.126004\pi$
$402$	−3.40918	+	1.64399i	−0.170035	+	0.0819947i
$403$	20.1736			1.00492
$404$	−0.670204	+	9.56774i	−0.0333439	+	0.476013i
$405$	8.09676	+	21.1020i	0.402331	+	1.04857i
$406$	−13.5799	+	12.6619i	−0.673960	+	0.628401i
$407$	−27.7676			−1.37639
$408$	28.5568	−	11.3858i	1.41377	−	0.563681i
$409$	9.02346			0.446181			0.223091	−	0.974798i	$-0.428385\pi$
$409$	9.02346			0.446181			0.223091	+	0.974798i	$0.428385\pi$
$410$	22.8826	−	21.3358i	1.13009	−	1.05370i
$411$	5.26963	+	1.63648i	0.259932	+	0.0807214i
$412$	−25.0089	−	1.75183i	−1.23210	−	0.0863064i
$413$	−33.5000			−1.64843
$414$	0.626542	+	4.19612i	0.0307929	+	0.206228i
$415$		−	23.7362i		−	1.16516i
$416$	−18.0926	+	12.6604i	−0.887061	+	0.620728i
$417$	−4.12233	+	13.2743i	−0.201871	+	0.650047i
$418$	4.67223	−	4.35640i	0.228526	−	0.213079i
$419$			15.4635i			0.755440i	0.925920	+	0.377720i	$0.123292\pi$
$419$			15.4635i			0.755440i	−0.925920	+	0.377720i	$0.876708\pi$
$420$	−8.74958	+	22.4890i	−0.426936	+	1.09735i
$421$			22.8596i			1.11411i	0.830476	+	0.557055i	$0.188069\pi$
$421$			22.8596i			1.11411i	−0.830476	+	0.557055i	$0.811931\pi$
$422$	−13.8039	−	14.8046i	−0.671961	−	0.720677i
$423$	11.9794	+	8.23454i	0.582461	+	0.400377i
$424$	24.8188	−	20.0904i	1.20531	−	0.975677i
$425$		−	8.20076i		−	0.397796i
$426$	2.39975	−	1.15722i	0.116268	−	0.0560674i
$427$	30.2774			1.46522
$428$	−4.95368	−	0.346996i	−0.239445	−	0.0167727i
$429$	−10.7516	+	34.6215i	−0.519094	+	1.67154i
$430$	−2.05447	−	2.20342i	−0.0990755	−	0.106258i
$431$	2.10031			0.101169			0.0505843	−	0.998720i	$-0.483892\pi$
$431$	2.10031			0.101169			0.0505843	+	0.998720i	$0.483892\pi$
$432$	−17.9582	+	10.4644i	−0.864012	+	0.503470i
$433$	−16.4973			−0.792810			−0.396405	−	0.918076i	$-0.629742\pi$
$433$	−16.4973			−0.792810			−0.396405	+	0.918076i	$0.629742\pi$
$434$	13.8250	+	14.8273i	0.663624	+	0.711735i
$435$	−6.10591	+	19.6617i	−0.292756	+	0.942706i
$436$	21.7800	+	1.52565i	1.04307	+	0.0730656i
$437$	−0.842460			−0.0403003
$438$	−4.39620	+	2.11995i	−0.210058	+	0.101295i
$439$			22.5716i			1.07728i	0.842535	+	0.538642i	$0.181063\pi$
$439$			22.5716i			1.07728i	−0.842535	+	0.538642i	$0.818937\pi$
$440$	−23.9626	−	29.6023i	−1.14237	−	1.41123i
$441$	1.71628	+	1.17975i	0.0817274	+	0.0561785i
$442$	−23.6254	−	25.3382i	−1.12374	−	1.20521i
$443$			10.7631i			0.511369i	0.966760	+	0.255684i	$0.0823008\pi$
$443$			10.7631i			0.511369i	−0.966760	+	0.255684i	$0.917699\pi$
$444$	−6.50474	+	16.7191i	−0.308701	+	0.793454i
$445$			28.8688i			1.36851i
$446$	9.17874	−	8.55828i	0.434626	−	0.405246i
$447$	−2.24536	+	7.23030i	−0.106202	+	0.341981i
$448$	−21.7042	−	4.62159i	−1.02543	−	0.218350i
$449$		−	11.6327i		−	0.548983i	−0.961589	−	0.274492i	$-0.911490\pi$
$449$		−	11.6327i		−	0.548983i	0.961589	−	0.274492i	$-0.0885096\pi$
$450$	0.818776	+	5.48357i	0.0385975	+	0.258498i
$451$	47.2327			2.22410
$452$	35.7317	+	2.50294i	1.68068	+	0.117729i
$453$	−3.16908	−	0.984153i	−0.148896	−	0.0462395i
$454$	−20.0256	+	18.6719i	−0.939848	+	0.876317i
$455$	27.1929			1.27482
$456$	−1.52853	−	3.83371i	−0.0715798	−	0.179530i
$457$	9.95554			0.465701			0.232850	−	0.972513i	$-0.425195\pi$
$457$	9.95554			0.465701			0.232850	+	0.972513i	$0.425195\pi$
$458$	0.223120	−	0.208038i	0.0104257	−	0.00972097i
$459$	−20.1845	−	25.6097i	−0.942131	−	1.19536i
$460$	−0.350970	+	5.01040i	−0.0163640	+	0.233611i
$461$	−17.9462			−0.835836			−0.417918	−	0.908485i	$-0.637240\pi$
$461$	−17.9462			−0.835836			−0.417918	+	0.908485i	$0.637240\pi$
$462$	−32.8145	+	15.8239i	−1.52667	+	0.736195i
$463$			5.96645i			0.277285i	0.990343	+	0.138642i	$0.0442738\pi$
$463$			5.96645i			0.277285i	−0.990343	+	0.138642i	$0.955726\pi$
$464$	−18.7476	−	2.63943i	−0.870336	−	0.122532i
$465$	21.4678	+	6.66679i	0.995546	+	0.309165i
$466$	−22.4985	+	20.9776i	−1.04222	+	0.971770i
$467$		−	18.7616i		−	0.868183i	−0.900869	−	0.434091i	$-0.857069\pi$
$467$		−	18.7616i		−	0.868183i	0.900869	−	0.434091i	$-0.142931\pi$
$468$	18.3273	+	14.5840i	0.847178	+	0.674144i
$469$			4.28605i			0.197911i
$470$	11.7360	+	12.5868i	0.541340	+	0.580586i
$471$	−19.5011	−	6.05605i	−0.898565	−	0.279048i
$472$	−21.4923	−	26.5506i	−0.989261	−	1.22209i
$473$		−	4.54814i		−	0.209124i
$474$	10.3913	+	21.5488i	0.477289	+	0.989768i
$475$	−1.10094			−0.0505147
$476$	2.43269	−	34.7287i	0.111502	−	1.59179i
$477$	−27.9102	−	19.1851i	−1.27792	−	0.878427i
$478$	15.5294	+	16.6552i	0.710297	+	0.761792i
$479$	−28.5826			−1.30597			−0.652986	−	0.757370i	$-0.726484\pi$
$479$	−28.5826			−1.30597			−0.652986	+	0.757370i	$0.726484\pi$
$480$	−23.4372	+	7.49355i	−1.06976	+	0.342032i
$481$	20.2162			0.921778
$482$	15.6775	+	16.8141i	0.714092	+	0.765862i
$483$	4.58828	+	1.42488i	0.208774	+	0.0648345i
$484$	2.48044	−	35.4105i	0.112747	−	1.60957i
$485$	23.2064			1.05375
$486$	16.0536	+	15.1090i	0.728204	+	0.685360i
$487$			23.9300i			1.08437i	0.840259	+	0.542186i	$0.182403\pi$
$487$			23.9300i			1.08437i	−0.840259	+	0.542186i	$0.817597\pi$
$488$	19.4248	+	23.9965i	0.879317	+	1.08627i
$489$	−1.41916	+	4.56985i	−0.0641766	+	0.206656i
$490$	1.68139	+	1.80329i	0.0759576	+	0.0814644i
$491$			16.5244i			0.745736i	0.927884	+	0.372868i	$0.121626\pi$
$491$			16.5244i			0.745736i	−0.927884	+	0.372868i	$0.878374\pi$
$492$	11.0646	−	28.4392i	0.498829	−	1.28214i
$493$		−	29.7021i		−	1.33772i
$494$	−3.40161	+	3.17167i	−0.153046	+	0.142700i
$495$	−22.8828	+	33.2895i	−1.02851	+	1.49625i
$496$	−2.88188	+	20.4697i	−0.129400	+	0.919119i
$497$		−	3.01699i		−	0.135330i
$498$	−10.0561	−	20.8536i	−0.450624	−	0.934472i
$499$	21.7769			0.974867			0.487433	−	0.873160i	$-0.337933\pi$
$499$	21.7769			0.974867			0.487433	+	0.873160i	$0.337933\pi$
$500$	1.29620	−	18.5043i	0.0579676	−	0.827538i
$501$	7.99988	−	25.7605i	0.357408	−	1.15089i
$502$	26.7552	−	24.9466i	1.19414	−	1.11342i
$503$	19.8079			0.883191			0.441596	−	0.897214i	$-0.354413\pi$
$503$	19.8079			0.883191			0.441596	+	0.897214i	$0.354413\pi$
$504$	1.84071	+	23.4648i	0.0819918	+	1.04520i
$505$	12.0434			0.535922
$506$	−5.54594	+	5.17105i	−0.246547	+	0.229881i
$507$	1.14981	−	3.70251i	0.0510647	−	0.164434i
$508$	4.32328	+	0.302838i	0.191815	+	0.0134363i
$509$	20.3438			0.901722			0.450861	−	0.892594i	$-0.351117\pi$
$509$	20.3438			0.901722			0.450861	+	0.892594i	$0.351117\pi$
$510$	−16.7675	−	34.7712i	−0.742477	−	1.53969i
$511$			5.52693i			0.244497i
$512$	−10.2617	−	20.1668i	−0.453506	−	0.891253i
$513$	−3.43806	+	2.70974i	−0.151794	+	0.119638i
$514$	−8.96873	+	8.36246i	−0.395594	+	0.368852i
$515$			31.4798i			1.38717i
$516$	−2.73848	−	1.06543i	−0.120555	−	0.0469030i
$517$			25.9808i			1.14263i
$518$	13.8542	+	14.8586i	0.608720	+	0.652851i
$519$	7.87177	−	25.3480i	0.345532	−	1.11265i
$520$	17.4459	+	21.5519i	0.765054	+	0.945113i
$521$		−	10.4933i		−	0.459720i	−0.973224	−	0.229860i	$-0.926173\pi$
$521$		−	10.4933i		−	0.459720i	0.973224	−	0.229860i	$-0.0738268\pi$
$522$	2.96550	+	19.8608i	0.129796	+	0.869282i
$523$	2.60085			0.113727			0.0568637	−	0.998382i	$-0.481890\pi$
$523$	2.60085			0.113727			0.0568637	+	0.998382i	$0.481890\pi$
$524$	−39.1606	−	2.74313i	−1.71074	−	0.119834i
$525$	5.99605	+	1.86206i	0.261689	+	0.0812671i
$526$	−23.6675	−	25.3834i	−1.03195	−	1.10677i
$527$	−32.4305			−1.41270
$528$	−33.5938	−	15.8553i	−1.46198	−	0.690013i
$529$	1.00000			0.0434783
$530$	−27.3429	−	29.3252i	−1.18770	−	1.27381i
$531$	−20.5238	+	29.8576i	−0.890657	+	1.29571i
$532$	−4.66228	−	0.326585i	−0.202136	−	0.0141592i
$533$	−34.3877			−1.48950
$534$	12.2306	+	25.3629i	0.529268	+	1.09756i
$535$			6.23542i			0.269581i
$536$	−3.39693	+	2.74976i	−0.146725	+	0.118772i
$537$	−17.4837	−	5.42953i	−0.754477	−	0.234302i
$538$	−17.4348	−	18.6987i	−0.751665	−	0.806160i
$539$			3.72222i			0.160328i
$540$	14.6834	+	21.5762i	0.631875	+	0.928492i
$541$		−	0.884347i		−	0.0380210i	−0.999819	−	0.0190105i	$-0.993948\pi$
$541$		−	0.884347i		−	0.0380210i	0.999819	−	0.0190105i	$-0.00605160\pi$
$542$	2.37198	−	2.21164i	0.101885	−	0.0949979i
$543$	−20.5246	−	6.37388i	−0.880795	−	0.273529i
$544$	29.0851	−	20.3525i	1.24701	−	0.872607i
$545$		−	27.4155i		−	1.17435i
$546$	23.8906	−	11.5206i	1.02242	−	0.493035i
$547$	−19.5888			−0.837555			−0.418778	−	0.908089i	$-0.637541\pi$
$547$	−19.5888			−0.837555			−0.418778	+	0.908089i	$0.637541\pi$
$548$	6.35593	+	0.445222i	0.271512	+	0.0190189i
$549$	18.5495	−	26.9854i	0.791672	−	1.15171i
$550$	−7.24754	+	6.75762i	−0.309036	+	0.288146i
$551$	−3.98747			−0.169872
$552$	1.81436	+	4.55061i	0.0772244	+	0.193687i
$553$	27.0913			1.15204
$554$	−23.7441	+	22.1391i	−1.00879	+	0.940599i
$555$	21.5131	+	6.68086i	0.913180	+	0.283587i
$556$	−1.12153	+	16.0108i	−0.0475633	+	0.679008i
$557$	−5.60516			−0.237498			−0.118749	−	0.992924i	$-0.537888\pi$
$557$	−5.60516			−0.237498			−0.118749	+	0.992924i	$0.537888\pi$
$558$	21.6852	−	3.23791i	0.918006	−	0.137072i
$559$			3.31127i			0.140052i
$560$	−3.88462	+	27.5921i	−0.164155	+	1.16598i
$561$	17.2840	−	55.6565i	0.729733	−	2.34982i
$562$	−1.31306	+	1.22430i	−0.0553880	+	0.0516439i
$563$			25.5536i			1.07696i	0.842640	+	0.538478i	$0.181000\pi$
$563$			25.5536i			1.07696i	−0.842640	+	0.538478i	$0.819000\pi$
$564$	15.6433	+	6.08617i	0.658700	+	0.256274i
$565$		−	44.9771i		−	1.89220i
$566$	0.00120328	+	0.00129052i	5.05777e−5	+	5.42445e-5i
$567$	23.3078	−	8.94311i	0.978834	−	0.375575i
$568$	2.39113	−	1.93558i	0.100330	−	0.0812151i
$569$			22.2667i			0.933470i	0.884397	+	0.466735i	$0.154570\pi$
$569$			22.2667i			0.933470i	−0.884397	+	0.466735i	$0.845430\pi$
$570$	−4.66799	+	2.25101i	−0.195520	+	0.0942845i
$571$	−16.9773			−0.710479			−0.355240	−	0.934775i	$-0.615601\pi$
$571$	−16.9773			−0.710479			−0.355240	+	0.934775i	$0.615601\pi$
$572$	−2.92511	+	41.7585i	−0.122305	+	1.74601i
$573$	5.67641	−	18.2787i	0.237135	−	0.763602i
$574$	−23.5660	−	25.2745i	−0.983627	−	1.05494i
$575$	1.30682			0.0544981
$576$	−17.4162	+	16.5129i	−0.725674	+	0.688039i
$577$	6.89737			0.287141			0.143571	−	0.989640i	$-0.454142\pi$
$577$	6.89737			0.287141			0.143571	+	0.989640i	$0.454142\pi$
$578$	21.5842	+	23.1490i	0.897784	+	0.962872i
$579$	13.0263	−	41.9461i	0.541355	−	1.74322i
$580$	−1.66118	+	23.7148i	−0.0689769	+	0.984705i
$581$	−26.2173			−1.08768
$582$	20.3882	−	9.83164i	0.845116	−	0.407535i
$583$		−	60.5310i		−	2.50694i
$584$	−4.38039	+	3.54586i	−0.181262	+	0.146729i
$585$	16.6598	−	24.2364i	0.688798	−	1.00205i
$586$	−11.3953	−	12.2214i	−0.470735	−	0.504863i
$587$			37.5667i			1.55055i	0.631627	+	0.775273i	$0.282387\pi$
$587$			37.5667i			1.55055i	−0.631627	+	0.775273i	$0.717613\pi$
$588$	2.24118	+	0.871955i	0.0924249	+	0.0359588i
$589$			4.35375i			0.179393i
$590$	−31.3714	+	29.2508i	−1.29154	+	1.20424i
$591$	4.86031	−	15.6508i	0.199927	−	0.643786i
$592$	−2.88796	+	20.5129i	−0.118694	+	0.843076i
$593$			41.7325i			1.71375i	0.515527	+	0.856873i	$0.327596\pi$
$593$			41.7325i			1.71375i	−0.515527	+	0.856873i	$0.672404\pi$
$594$	−6.00041	+	38.9412i	−0.246200	+	1.59778i
$595$	−43.7146			−1.79212
$596$	−0.610875	+	8.72078i	−0.0250224	+	0.357217i
$597$	−3.04865	−	0.946753i	−0.124773	−	0.0387480i
$598$	4.03772	−	3.76478i	0.165115	−	0.153953i
$599$	37.4802			1.53140			0.765700	−	0.643198i	$-0.222393\pi$
$599$	37.4802			1.53140			0.765700	+	0.643198i	$0.222393\pi$
$600$	2.37104	+	5.94682i	0.0967973	+	0.242778i
$601$	31.6815			1.29231			0.646157	−	0.763205i	$-0.276375\pi$
$601$	31.6815			1.29231			0.646157	+	0.763205i	$0.276375\pi$
$602$	−2.43374	+	2.26923i	−0.0991919	+	0.0924867i
$603$	3.82004	+	2.62585i	0.155564	+	0.106933i
$604$	−3.82237	−	0.267750i	−0.155530	−	0.0108946i
$605$	−44.5728			−1.81214
$606$	10.5808	−	5.10230i	0.429815	−	0.207267i
$607$			15.7689i			0.640041i	0.947411	+	0.320020i	$0.103690\pi$
$607$			15.7689i			0.640041i	−0.947411	+	0.320020i	$0.896310\pi$
$608$	−2.73230	−	3.90464i	−0.110809	−	0.158354i
$609$	21.7169	+	6.74415i	0.880014	+	0.273287i
$610$	28.3536	−	26.4369i	1.14800	−	1.07040i
$611$		−	18.9153i		−	0.765230i
$612$	−29.4624	−	23.4448i	−1.19095	−	0.947699i
$613$			29.1580i			1.17768i	0.808249	+	0.588841i	$0.200416\pi$
$613$			29.1580i			1.17768i	−0.808249	+	0.588841i	$0.799584\pi$
$614$	−6.84472	−	7.34095i	−0.276230	−	0.296257i
$615$	−36.5938	−	11.3641i	−1.47560	−	0.458246i
$616$	−32.6966	+	26.4673i	−1.31738	+	1.06640i
$617$		−	41.0505i		−	1.65263i	−0.563209	−	0.826315i	$-0.690433\pi$
$617$		−	41.0505i		−	1.65263i	0.563209	−	0.826315i	$-0.309567\pi$
$618$	13.3368	+	27.6568i	0.536483	+	1.11252i
$619$	−16.5210			−0.664035			−0.332017	−	0.943273i	$-0.607729\pi$
$619$	−16.5210			−0.664035			−0.332017	+	0.943273i	$0.607729\pi$
$620$	25.8933	+	1.81378i	1.03990	+	0.0728431i
$621$	4.08098	−	3.21646i	0.163764	−	0.129072i
$622$	22.8450	+	24.5013i	0.916002	+	0.982411i
$623$	31.8864			1.27750
$624$	24.4579	+	11.5434i	0.979101	+	0.462107i
$625$	−29.8263			−1.19305
$626$	−27.0221	−	28.9811i	−1.08002	−	1.15832i
$627$	−7.47181	−	2.32036i	−0.298395	−	0.0926662i
$628$	−23.5212	−	1.64762i	−0.938597	−	0.0657471i
$629$	−32.4989			−1.29582
$630$	29.2304	−	4.36453i	1.16457	−	0.173887i
$631$		−	21.9008i		−	0.871857i	−0.899981	−	0.435928i	$-0.856420\pi$
$631$		−	21.9008i		−	0.871857i	0.899981	−	0.435928i	$-0.143580\pi$
$632$	17.3807	+	21.4713i	0.691367	+	0.854083i
$633$	−7.35237	+	23.6755i	−0.292231	+	0.941015i
$634$	−29.7175	−	31.8720i	−1.18023	−	1.26580i
$635$		−	5.44191i		−	0.215956i
$636$	−36.4463	−	14.1798i	−1.44519	−	0.562265i
$637$		−	2.70996i		−	0.107373i
$638$	−26.2496	+	24.4752i	−1.03923	+	0.968983i
$639$	−2.68896	−	1.84836i	−0.106374	−	0.0731201i
$640$	−24.3605	+	14.6232i	−0.962933	+	0.578034i
$641$		−	19.1406i		−	0.756010i	−0.925804	−	0.378005i	$-0.876610\pi$
$641$		−	19.1406i		−	0.756010i	0.925804	−	0.378005i	$-0.123390\pi$
$642$	2.64170	+	5.47817i	0.104260	+	0.216206i
$643$	−5.41810			−0.213669			−0.106834	−	0.994277i	$-0.534071\pi$
$643$	−5.41810			−0.213669			−0.106834	+	0.994277i	$0.534071\pi$
$644$	5.53413	+	0.387656i	0.218075	+	0.0152758i
$645$	−1.09428	+	3.52370i	−0.0430872	+	0.138745i
$646$	5.46834	−	5.09869i	0.215149	−	0.200605i
$647$	32.3854			1.27320			0.636600	−	0.771194i	$-0.280340\pi$
$647$	32.3854			1.27320			0.636600	+	0.771194i	$0.280340\pi$
$648$	22.0412	+	12.7351i	0.865862	+	0.500284i
$649$	−64.7546			−2.54184
$650$	5.27656	−	4.91988i	0.206964	−	0.192973i
$651$	7.36366	−	23.7118i	0.288605	−	0.929339i
$652$	−0.386098	+	5.51189i	−0.0151208	+	0.215862i
$653$	26.8532			1.05085			0.525424	−	0.850840i	$-0.323907\pi$
$653$	26.8532			1.05085			0.525424	+	0.850840i	$0.323907\pi$
$654$	−11.6149	−	24.0861i	−0.454178	−	0.941842i
$655$			49.2933i			1.92605i
$656$	4.91242	−	34.8925i	0.191798	−	1.36232i
$657$	4.92601	+	3.38608i	0.192182	+	0.132104i
$658$	13.9025	−	12.9627i	0.541976	−	0.505339i
$659$		−	8.49860i		−	0.331058i	−0.986205	−	0.165529i	$-0.947067\pi$
$659$		−	8.49860i		−	0.331058i	0.986205	−	0.165529i	$-0.0529332\pi$
$660$	−16.9127	+	43.4708i	−0.658327	+	1.69210i
$661$			4.60985i			0.179302i	0.995973	+	0.0896511i	$0.0285752\pi$
$661$			4.60985i			0.179302i	−0.995973	+	0.0896511i	$0.971425\pi$
$662$	−29.0431	−	31.1487i	−1.12879	−	1.21063i
$663$	−12.5836	+	40.5207i	−0.488707	+	1.57369i
$664$	−16.8200	−	20.7786i	−0.652741	−	0.806367i
$665$			5.86863i			0.227576i
$666$	21.7309	−	3.24474i	0.842056	−	0.125731i
$667$	4.73312			0.183267
$668$	2.17646	−	31.0709i	0.0842097	−	1.20217i
$669$	−14.6786	−	4.55841i	−0.567507	−	0.176238i
$670$	3.74240	+	4.01372i	0.144582	+	0.155064i
$671$	58.5254			2.25935
$672$	8.27684	+	25.8870i	0.319286	+	0.998614i
$673$	9.40419			0.362505			0.181252	−	0.983437i	$-0.441985\pi$
$673$	9.40419			0.362505			0.181252	+	0.983437i	$0.441985\pi$
$674$	−1.77024	−	1.89858i	−0.0681871	−	0.0731306i
$675$	5.33310	−	4.20333i	0.205271	−	0.161786i
$676$	0.312818	−	4.46576i	0.0120315	−	0.171760i
$677$	−29.7336			−1.14276			−0.571378	−	0.820687i	$-0.693591\pi$
$677$	−29.7336			−1.14276			−0.571378	+	0.820687i	$0.693591\pi$
$678$	−19.0550	−	39.5150i	−0.731805	−	1.51756i
$679$		−	25.6321i		−	0.983671i
$680$	−28.0456	−	34.6462i	−1.07550	−	1.32862i
$681$	32.0248	+	9.94526i	1.22719	+	0.381103i
$682$	26.7235	+	28.6609i	1.02329	+	1.09748i
$683$		−	7.45395i		−	0.285218i	−0.989779	−	0.142609i	$-0.954451\pi$
$683$		−	7.45395i		−	0.285218i	0.989779	−	0.142609i	$-0.0455491\pi$
$684$	−3.14743	+	3.95529i	−0.120345	+	0.151234i
$685$		−	8.00050i		−	0.305684i
$686$	−18.0921	+	16.8691i	−0.690758	+	0.644065i
$687$	−0.356813	−	0.110808i	−0.0136133	−	0.00422757i
$688$	−3.35988	−	0.473028i	−0.128094	−	0.0180340i
$689$			44.0695i			1.67892i
$690$	5.54090	−	2.67195i	0.210938	−	0.101719i
$691$	−30.2586			−1.15109			−0.575545	−	0.817770i	$-0.695210\pi$
$691$	−30.2586			−1.15109			−0.575545	+	0.817770i	$0.695210\pi$
$692$	2.14161	−	30.5733i	0.0814116	−	1.16222i
$693$	36.7692	+	25.2747i	1.39675	+	0.960107i
$694$	4.59280	−	4.28234i	0.174340	−	0.162555i
$695$	20.1535			0.764465
$696$	8.58760	+	21.5386i	0.325512	+	0.816419i
$697$	55.2807			2.09391
$698$	34.7177	−	32.3709i	1.31408	−	1.22525i
$699$	35.9795	+	11.1734i	1.36087	+	0.422615i
$700$	7.23210	+	0.506596i	0.273348	+	0.0191475i
$701$	13.5932			0.513409			0.256705	−	0.966490i	$-0.417363\pi$
$701$	13.5932			0.513409			0.256705	+	0.966490i	$0.417363\pi$
$702$	4.36859	−	28.3511i	0.164882	−	1.07004i
$703$			4.36294i			0.164551i
$704$	−41.9536	−	8.93342i	−1.58119	−	0.336691i
$705$	6.25095	−	20.1288i	0.235424	−	0.758093i
$706$	−11.8291	+	11.0295i	−0.445195	+	0.415101i
$707$		−	13.3022i		−	0.500282i
$708$	−15.1692	+	38.9894i	−0.570093	+	1.46531i
$709$		−	1.17145i		−	0.0439949i	−0.999758	−	0.0219974i	$-0.992997\pi$
$709$		−	1.17145i		−	0.0439949i	0.999758	−	0.0219974i	$-0.00700256\pi$
$710$	−2.63431	−	2.82529i	−0.0988639	−	0.106031i
$711$	16.5975	−	24.1457i	0.622455	−	0.905536i
$712$	20.4570	+	25.2717i	0.766660	+	0.947097i
$713$		−	5.16790i		−	0.193539i
$714$	−38.4058	+	18.5202i	−1.43730	+	0.693100i
$715$	52.5633			1.96576
$716$	−21.0879	−	1.47717i	−0.788090	−	0.0552043i
$717$	8.27143	−	26.6349i	0.308902	−	0.994700i
$718$	−14.6807	−	15.7451i	−0.547880	−	0.587601i
$719$	−17.5844			−0.655787			−0.327893	−	0.944715i	$-0.606339\pi$
$719$	−17.5844			−0.655787			−0.327893	+	0.944715i	$0.606339\pi$
$720$	22.2122	+	20.3666i	0.827801	+	0.759019i
$721$	34.7704			1.29492
$722$	17.6397	+	18.9185i	0.656480	+	0.704074i
$723$	8.35035	−	26.8891i	0.310553	−	1.00001i
$724$	−24.7556	−	1.73409i	−0.920035	−	0.0644469i
$725$	6.18533			0.229717
$726$	−39.1597	+	18.8837i	−1.45335	+	0.700841i
$727$		−	32.7972i		−	1.21638i	−0.793791	−	0.608190i	$-0.791896\pi$
$727$		−	32.7972i		−	1.21638i	0.793791	−	0.608190i	$-0.208104\pi$
$728$	23.8047	−	19.2695i	0.882260	−	0.714176i
$729$	6.30878	−	26.2526i	0.233658	−	0.972319i
$730$	4.82589	+	5.17576i	0.178614	+	0.191563i
$731$		−	5.32310i		−	0.196882i
$732$	13.7100	−	35.2387i	0.506735	−	1.30246i
$733$			32.7003i			1.20781i	0.797054	+	0.603907i	$0.206390\pi$
$733$			32.7003i			1.20781i	−0.797054	+	0.603907i	$0.793610\pi$
$734$	11.7820	−	10.9856i	0.434882	−	0.405485i
$735$	0.895564	−	2.88381i	0.0330334	−	0.106371i
$736$	3.24324	+	4.63480i	0.119547	+	0.170841i
$737$			8.28483i			0.305176i
$738$	−36.9643	+	5.51930i	−1.36067	+	0.203168i
$739$	−12.7460			−0.468869			−0.234434	−	0.972132i	$-0.575324\pi$
$739$	−12.7460			−0.468869			−0.234434	+	0.972132i	$0.575324\pi$
$740$	25.9479	+	1.81760i	0.953863	+	0.0668165i
$741$	5.43984	+	1.68933i	0.199838	+	0.0620592i
$742$	−32.3906	+	30.2010i	−1.18910	+	1.10872i
$743$	−41.4428			−1.52039			−0.760195	−	0.649695i	$-0.774897\pi$
$743$	−41.4428			−1.52039			−0.760195	+	0.649695i	$0.774897\pi$
$744$	23.5171	−	9.37645i	0.862180	−	0.343757i
$745$	10.9772			0.402175
$746$	25.9473	−	24.1933i	0.949998	−	0.885780i
$747$	−16.0621	+	23.3668i	−0.587680	+	0.854946i
$748$	4.70232	−	67.1297i	0.171934	−	2.45451i
$749$	6.88720			0.251653
$750$	−20.4636	+	9.86800i	−0.747223	+	0.360329i
$751$			27.5421i			1.00503i	0.864570	+	0.502513i	$0.167591\pi$
$751$			27.5421i			1.00503i	−0.864570	+	0.502513i	$0.832409\pi$
$752$	19.1929	+	2.70212i	0.699895	+	0.0985363i
$753$	−42.7867	−	13.2873i	−1.55924	−	0.484218i
$754$	19.1110	−	17.8191i	0.695982	−	0.648935i
$755$			4.81139i			0.175104i
$756$	23.8315	−	16.2183i	0.866745	−	0.589853i
$757$			16.9574i			0.616327i	0.951333	+	0.308164i	$0.0997144\pi$
$757$			16.9574i			0.616327i	−0.951333	+	0.308164i	$0.900286\pi$
$758$	−6.73807	−	7.22658i	−0.244738	−	0.262481i
$759$	8.86904	+	2.75427i	0.321926	+	0.0999735i
$760$	−4.65121	+	3.76508i	−0.168717	+	0.136574i
$761$		−	21.9704i		−	0.796425i	−0.917293	−	0.398212i	$-0.869631\pi$
$761$		−	21.9704i		−	0.796425i	0.917293	−	0.398212i	$-0.130369\pi$
$762$	−2.30552	−	4.78103i	−0.0835204	−	0.173199i
$763$	−30.2812			−1.09625
$764$	1.54433	−	22.0467i	0.0558720	−	0.797621i
$765$	−26.7818	+	38.9617i	−0.968298	+	1.40866i
$766$	−25.3437	−	27.1811i	−0.915704	−	0.982091i
$767$	47.1445			1.70229
$768$	−15.2068	+	23.1679i	−0.548728	+	0.836001i
$769$	21.3273			0.769081			0.384541	−	0.923108i	$-0.374360\pi$
$769$	21.3273			0.769081			0.384541	+	0.923108i	$0.374360\pi$
$770$	36.0218	+	38.6334i	1.29814	+	1.39225i
$771$	14.3427	+	4.45411i	0.516541	+	0.160411i
$772$	3.54396	−	50.5931i	0.127550	−	1.82088i
$773$	0.548391			0.0197243			0.00986213	−	0.999951i	$-0.496861\pi$
$773$	0.548391			0.0197243			0.00986213	+	0.999951i	$0.496861\pi$
$774$	0.531466	+	3.55937i	0.0191032	+	0.127939i
$775$		−	6.75351i		−	0.242593i
$776$	20.3149	−	16.4446i	0.729261	−	0.590325i
$777$	7.37920	−	23.7618i	0.264727	−	0.852451i
$778$	−5.29893	−	5.68309i	−0.189976	−	0.203749i
$779$		−	7.42136i		−	0.265898i
$780$	12.3133	−	31.6488i	0.440887	−	1.13321i
$781$		−	5.83176i		−	0.208677i
$782$	−6.49092	+	6.05215i	−0.232115	+	0.216424i
$783$	19.3158	−	15.2239i	0.690289	−	0.544058i
$784$	2.74974	+	0.387129i	0.0982051	+	0.0138260i
$785$			29.6072i			1.05673i
$786$	20.8836	+	43.3069i	0.744894	+	1.54471i
$787$	20.3708			0.726141			0.363071	−	0.931762i	$-0.381728\pi$
$787$	20.3708			0.726141			0.363071	+	0.931762i	$0.381728\pi$
$788$	1.32230	−	18.8771i	0.0471052	−	0.672467i
$789$	−12.6061	+	40.5930i	−0.448789	+	1.44515i
$790$	25.3699	−	23.6550i	0.902622	−	0.841607i
$791$	−49.6785			−1.76637
$792$	3.55805	+	45.3568i	0.126430	+	1.61168i
$793$	−42.6094			−1.51310
$794$	−25.6641	+	23.9293i	−0.910786	+	0.849219i
$795$	−14.5637	+	46.8968i	−0.516522	+	1.66326i
$796$	−3.67711	−	0.257575i	−0.130332	−	0.00912951i
$797$	37.5834			1.33127			0.665637	−	0.746276i	$-0.268160\pi$
$797$	37.5834			1.33127			0.665637	+	0.746276i	$0.268160\pi$
$798$	2.48631	+	5.15593i	0.0880143	+	0.182518i
$799$			30.4077i			1.07575i
$800$	4.23832	+	6.05684i	0.149847	+	0.214142i
$801$	19.5352	−	28.4195i	0.690244	−	1.00415i
$802$	−15.9736	+	14.8938i	−0.564046	+	0.525918i
$803$			10.6834i			0.377010i
$804$	4.98837	+	1.94078i	0.175926	+	0.0684459i
$805$		−	6.96606i		−	0.245521i
$806$	−19.4560	−	20.8665i	−0.685308	−	0.734992i
$807$	−9.28630	+	29.9029i	−0.326893	+	1.05263i
$808$	10.5427	−	8.53418i	0.370893	−	0.300232i
$809$			41.1621i			1.44718i	0.690228	+	0.723592i	$0.257510\pi$
$809$			41.1621i			1.44718i	−0.690228	+	0.723592i	$0.742490\pi$
$810$	14.0181	−	28.7263i	0.492545	−	1.00934i
$811$	28.9045			1.01497			0.507487	−	0.861659i	$-0.330574\pi$
$811$	28.9045			1.01497			0.507487	+	0.861659i	$0.330574\pi$
$812$	26.1937	+	1.83482i	0.919219	+	0.0643897i
$813$	−3.79325	−	1.17799i	−0.133035	−	0.0413138i
$814$	26.7799	+	28.7214i	0.938634	+	1.00668i
$815$	6.93807			0.243030
$816$	−39.3179	−	18.5569i	−1.37640	−	0.649621i
$817$	−0.714619			−0.0250014
$818$	−8.70249	−	9.33340i	−0.304275	−	0.326335i
$819$	−26.7697	−	18.4012i	−0.935411	−	0.642991i
$820$	−44.1374	−	3.09175i	−1.54134	−	0.107968i
$821$	4.91129			0.171405			0.0857026	−	0.996321i	$-0.472687\pi$
$821$	4.91129			0.171405			0.0857026	+	0.996321i	$0.472687\pi$
$822$	−3.38950	−	7.02890i	−0.118222	−	0.245161i
$823$		−	55.9620i		−	1.95071i	−0.220636	−	0.975356i	$-0.570813\pi$
$823$		−	55.9620i		−	1.95071i	0.220636	−	0.975356i	$-0.429187\pi$
$824$	22.3073	+	27.5574i	0.777111	+	0.960008i
$825$	11.5902	+	3.59932i	0.403520	+	0.125312i
$826$	32.3083	+	34.6507i	1.12415	+	1.20565i
$827$			29.5676i			1.02817i	0.857740	+	0.514084i	$0.171868\pi$
$827$			29.5676i			1.02817i	−0.857740	+	0.514084i	$0.828132\pi$
$828$	3.73600	−	4.69492i	0.129835	−	0.163160i
$829$		−	7.37856i		−	0.256268i	−0.991757	−	0.128134i	$-0.959101\pi$
$829$		−	7.37856i		−	0.256268i	0.991757	−	0.128134i	$-0.0408987\pi$
$830$	−24.5515	+	22.8919i	−0.852194	+	0.794588i
$831$	37.9715	+	11.7920i	1.31722	+	0.409059i
$832$	30.5443	+	6.50396i	1.05893	+	0.225484i
$833$			4.35646i			0.150942i
$834$	17.7060	−	8.53824i	0.613108	−	0.295655i
$835$	−39.1103			−1.35347
$836$	−9.01207	−	0.631280i	−0.311689	−	0.0218333i
$837$	−16.6223	−	21.0901i	−0.574552	−	0.728981i
$838$	15.9946	−	14.9134i	0.552525	−	0.515176i
$839$	−11.8529			−0.409208			−0.204604	−	0.978845i	$-0.565591\pi$
$839$	−11.8529			−0.409208			−0.204604	+	0.978845i	$0.565591\pi$
$840$	31.6999	−	12.6390i	1.09375	−	0.436085i
$841$	−6.59755			−0.227502
$842$	23.6448	−	22.0465i	0.814854	−	0.759772i
$843$	2.09984	+	0.652100i	0.0723222	+	0.0224595i
$844$	−2.00030	+	28.5560i	−0.0688531	+	0.982938i
$845$	−5.62125			−0.193377
$846$	−3.03594	−	20.3325i	−0.104378	−	0.699047i
$847$			49.2319i			1.69163i
$848$	−44.7165	−	6.29551i	−1.53557	−	0.216189i
$849$	0.000640906	−	0.00206379i	2.19958e−5	−	7.08291e-5i
$850$	−8.48245	+	7.90905i	−0.290946	+	0.271278i
$851$		−	5.17881i		−	0.177527i
$852$	−3.51136	−	1.36613i	−0.120297	−	0.0468028i
$853$		−	38.0802i		−	1.30384i	−0.758287	−	0.651921i	$-0.773963\pi$
$853$		−	38.0802i		−	1.30384i	0.758287	−	0.651921i	$-0.226037\pi$
$854$	−29.2004	−	31.3174i	−0.999216	−	1.07166i
$855$	5.23055	+	3.59542i	0.178881	+	0.122961i
$856$	4.41855	+	5.45848i	0.151023	+	0.186567i
$857$		−	0.632531i		−	0.0216069i	−0.999942	−	0.0108034i	$-0.996561\pi$
$857$		−	0.632531i		−	0.0216069i	0.999942	−	0.0108034i	$-0.00343891\pi$
$858$	46.1799	−	22.2690i	1.57655	−	0.760251i
$859$	14.6868			0.501107			0.250553	−	0.968103i	$-0.419387\pi$
$859$	14.6868			0.501107			0.250553	+	0.968103i	$0.419387\pi$
$860$	−0.297711	+	4.25008i	−0.0101519	+	0.144927i
$861$	−12.5520	+	40.4189i	−0.427772	+	1.37747i
$862$	−2.02560	−	2.17246i	−0.0689923	−	0.0739941i
$863$	−50.3161			−1.71278			−0.856390	−	0.516330i	$-0.827298\pi$
$863$	−50.3161			−1.71278			−0.856390	+	0.516330i	$0.827298\pi$
$864$	28.1432	+	8.48279i	0.957453	+	0.288591i
$865$	−38.4840			−1.30849
$866$	15.9105	+	17.0640i	0.540660	+	0.579858i
$867$	11.4964	−	37.0198i	0.390439	−	1.25726i
$868$	2.00337	−	28.5998i	0.0679988	−	0.970742i
$869$	52.3668			1.77642
$870$	26.2258	−	12.6467i	0.889137	−	0.428762i
$871$		−	6.03176i		−	0.204378i
$872$	−19.4272	−	23.9995i	−0.657889	−	0.812727i
$873$	−22.8452	−	15.7036i	−0.773194	−	0.531485i
$874$	0.812493	+	0.871397i	0.0274830	+	0.0294754i
$875$			25.7269i			0.869729i
$876$	6.43259	+	2.50266i	0.217337	+	0.0845571i
$877$		−	40.6504i		−	1.37267i	−0.727287	−	0.686334i	$-0.759219\pi$
$877$		−	40.6504i		−	1.37267i	0.727287	−	0.686334i	$-0.240781\pi$
$878$	23.3469	−	21.7687i	0.787920	−	0.734659i
$879$	−6.06950	+	19.5445i	−0.204719	+	0.659218i
$880$	−7.50888	+	53.3349i	−0.253124	+	1.79792i
$881$			31.6700i			1.06699i	0.845804	+	0.533494i	$0.179121\pi$
$881$			31.6700i			1.06699i	−0.845804	+	0.533494i	$0.820879\pi$
$882$	−0.434955	−	2.91301i	−0.0146457	−	0.0980862i
$883$	−42.6968			−1.43686			−0.718431	−	0.695599i	$-0.755139\pi$
$883$	−42.6968			−1.43686			−0.718431	+	0.695599i	$0.755139\pi$
$884$	−3.42352	+	48.8737i	−0.115145	+	1.64380i
$885$	50.1690	+	15.5799i	1.68641	+	0.523713i
$886$	11.1328	−	10.3802i	0.374012	−	0.348730i
$887$	−37.2519			−1.25080			−0.625398	−	0.780306i	$-0.715063\pi$
$887$	−37.2519			−1.25080			−0.625398	+	0.780306i	$0.715063\pi$
$888$	23.5668	−	9.39623i	0.790849	−	0.315317i
$889$	−6.01075			−0.201594
$890$	29.8604	−	27.8419i	1.00092	−	0.933262i
$891$	45.0533	−	17.2868i	1.50934	−	0.579130i
$892$	−17.7045	−	1.24017i	−0.592790	−	0.0415239i
$893$	4.08219			0.136605
$894$	9.64414	−	4.65063i	0.322548	−	0.155540i
$895$			26.5442i			0.887276i
$896$	16.1518	+	26.9069i	0.539593	+	0.898895i
$897$	−6.45709	−	2.00524i	−0.215596	−	0.0669530i
$898$	−12.0323	+	11.2190i	−0.401524	+	0.374381i
$899$		−	24.4603i		−	0.815797i
$900$	4.88227	−	6.13541i	0.162742	−	0.204514i
$901$		−	70.8450i		−	2.36019i
$902$	−45.5526	−	48.8551i	−1.51673	−	1.62670i
$903$	3.89203	+	1.20866i	0.129518	+	0.0402217i
$904$	−31.8718	−	39.3729i	−1.06004	−	1.30952i
$905$			31.1610i			1.03583i
$906$	2.03840	+	4.22708i	0.0677212	+	0.140435i
$907$	37.5053			1.24534			0.622672	−	0.782483i	$-0.286047\pi$
$907$	37.5053			1.24534			0.622672	+	0.782483i	$0.286047\pi$
$908$	38.6265	+	2.70572i	1.28187	+	0.0897926i
$909$	−11.8559	−	8.14963i	−0.393236	−	0.270306i
$910$	−26.2257	−	28.1270i	−0.869372	−	0.932401i
$911$	24.3754			0.807592			0.403796	−	0.914849i	$-0.367690\pi$
$911$	24.3754			0.807592			0.403796	+	0.914849i	$0.367690\pi$
$912$	−2.49124	+	5.27837i	−0.0824931	+	0.174784i
$913$	−50.6774			−1.67718
$914$	−9.60141	−	10.2975i	−0.317586	−	0.340611i
$915$	−45.3429	−	14.0812i	−1.49899	−	0.465509i
$916$	−0.430367	−	0.0301465i	−0.0142197	−	0.000996068i
$917$	54.4458			1.79796
$918$	−7.02282	+	45.5765i	−0.231788	+	1.50425i
$919$			23.9382i			0.789648i	0.918757	+	0.394824i	$0.129194\pi$
$919$			23.9382i			0.789648i	−0.918757	+	0.394824i	$0.870806\pi$
$920$	5.52098	−	4.46915i	0.182021	−	0.147343i
$921$	−3.64571	+	11.7396i	−0.120130	+	0.386833i
$922$	17.3078	+	18.5626i	0.570002	+	0.611326i
$923$			4.24581i			0.139753i
$924$	48.0147	+	18.6806i	1.57957	+	0.614547i
$925$		−	6.76776i		−	0.222522i
$926$	6.17139	−	5.75422i	0.202805	−	0.189095i
$927$	21.3021	−	30.9899i	0.699653	−	1.01784i
$928$	15.3506	+	21.9371i	0.503910	+	0.720120i
$929$		−	24.2050i		−	0.794141i	−0.917788	−	0.397071i	$-0.870027\pi$
$929$		−	24.2050i		−	0.794141i	0.917788	−	0.397071i	$-0.129973\pi$
$930$	−13.8084	−	28.6348i	−0.452795	−	0.938973i
$931$	0.584848			0.0191676
$932$	43.3964	+	3.03984i	1.42150	+	0.0995733i
$933$	12.1680	−	39.1823i	0.398362	−	1.28277i
$934$	−19.4060	+	18.0942i	−0.634985	+	0.592061i
$935$	−84.4993			−2.76342
$936$	−2.59043	−	33.0220i	−0.0846710	−	1.07936i
$937$	24.2539			0.792340			0.396170	−	0.918177i	$-0.370339\pi$
$937$	24.2539			0.792340			0.396170	+	0.918177i	$0.370339\pi$
$938$	4.43327	−	4.13359i	0.144751	−	0.134967i
$939$	−14.3928	+	46.3464i	−0.469692	+	1.51246i
$940$	1.70064	−	24.2782i	0.0554689	−	0.791866i
$941$	−28.9009			−0.942143			−0.471071	−	0.882095i	$-0.656133\pi$
$941$	−28.9009			−0.942143			−0.471071	+	0.882095i	$0.656133\pi$
$942$	12.5434	+	26.0116i	0.408686	+	0.847504i
$943$			8.80915i			0.286865i
$944$	−6.73479	+	47.8366i	−0.219199	+	1.55695i
$945$	−22.4061	−	28.4284i	−0.728869	−	0.924774i
$946$	−4.70436	+	4.38636i	−0.152952	+	0.142613i
$947$		−	29.3765i		−	0.954607i	−0.878739	−	0.477303i	$-0.841614\pi$
$947$		−	29.3765i		−	0.954607i	0.878739	−	0.477303i	$-0.158386\pi$
$948$	12.2673	−	31.5305i	0.398422	−	1.02406i
$949$		−	7.77805i		−	0.252486i
$950$	1.06178	+	1.13876i	0.0344487	+	0.0369462i
$951$	−15.8285	+	50.9695i	−0.513274	+	1.65280i
$952$	−38.2677	+	30.9771i	−1.24026	+	1.00397i
$953$			44.6274i			1.44562i	0.691045	+	0.722811i	$0.257150\pi$
$953$			44.6274i			1.44562i	−0.691045	+	0.722811i	$0.742850\pi$
$954$	7.07326	+	47.3716i	0.229005	+	1.53371i
$955$	−27.7512			−0.898007
$956$	2.25034	−	32.1256i	0.0727812	−	1.03901i
$957$	41.9783	+	13.0363i	1.35696	+	0.421403i
$958$	27.5659	+	29.5644i	0.890613	+	0.955181i
$959$	−8.83679			−0.285355
$960$	30.3544	+	17.0152i	0.979685	+	0.549164i
$961$	4.29278			0.138477
$962$	−19.4970	−	20.9106i	−0.628610	−	0.674183i
$963$	4.21945	−	6.13838i	0.135970	−	0.197806i
$964$	2.27181	−	32.4321i	0.0731701	−	1.04457i
$965$	−63.6838			−2.05005
$966$	−2.95125	−	6.12008i	−0.0949548	−	0.196910i
$967$		−	21.0680i		−	0.677502i	−0.940876	−	0.338751i	$-0.889996\pi$
$967$		−	21.0680i		−	0.677502i	0.940876	−	0.338751i	$-0.110004\pi$
$968$	−39.0190	+	31.5852i	−1.25412	+	1.01519i
$969$	−8.74494	−	2.71573i	−0.280928	−	0.0872417i
$970$	−22.3809	−	24.0035i	−0.718608	−	0.770706i
$971$		−	12.6458i		−	0.405824i	−0.979197	−	0.202912i	$-0.934959\pi$
$971$		−	12.6458i		−	0.405824i	0.979197	−	0.202912i	$-0.0650405\pi$
$972$	0.145497	−	31.1766i	0.00466682	−	0.999989i
$973$		−	22.2601i		−	0.713626i
$974$	24.7519	−	23.0788i	0.793104	−	0.739491i
$975$	−8.43824	−	2.62048i	−0.270240	−	0.0839226i
$976$	6.08692	−	43.2349i	0.194838	−	1.38391i
$977$			9.11515i			0.291620i	0.989313	+	0.145810i	$0.0465788\pi$
$977$			9.11515i			0.291620i	−0.989313	+	0.145810i	$0.953421\pi$
$978$	6.09549	−	2.93939i	0.194912	−	0.0939913i
$979$	61.6356			1.96988
$980$	0.243648	−	3.47829i	0.00778306	−	0.111110i
$981$	−18.5518	+	26.9889i	−0.592315	+	0.861688i
$982$	17.0920	−	15.9366i	0.545428	−	0.508558i
$983$	−5.61499			−0.179090			−0.0895452	−	0.995983i	$-0.528541\pi$
$983$	−5.61499			−0.179090			−0.0895452	+	0.995983i	$0.528541\pi$
$984$	−40.0871	+	15.9830i	−1.27793	+	0.509519i
$985$	−23.7614			−0.757101
$986$	−30.7223	+	28.6456i	−0.978398	+	0.912260i
$987$	−22.2328	−	6.90436i	−0.707677	−	0.219768i
$988$	6.56123	+	0.459603i	0.208741	+	0.0146219i
$989$	0.848253			0.0269729
$990$	56.5017	−	8.43653i	1.79574	−	0.268131i
$991$		−	5.97647i		−	0.189849i	−0.995484	−	0.0949244i	$-0.969739\pi$
$991$		−	5.97647i		−	0.189849i	0.995484	−	0.0949244i	$-0.0302609\pi$
$992$	23.9522	−	16.7607i	0.760484	−	0.532154i
$993$	−15.4693	+	49.8128i	−0.490903	+	1.58076i
$994$	−3.12062	+	2.90967i	−0.0989800	+	0.0922892i
$995$			4.62855i			0.146735i
$996$	−11.8715	+	30.5133i	−0.376163	+	0.966851i
$997$			13.6774i			0.433169i	0.976264	+	0.216584i	$0.0694916\pi$
$997$			13.6774i			0.433169i	−0.976264	+	0.216584i	$0.930508\pi$
$998$	−21.0022	−	22.5249i	−0.664814	−	0.713012i
$999$	−16.6574	−	21.1346i	−0.527018	−	0.668669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.j.d.323.13	yes	42
3.2	odd	2		552.2.j.c.323.30	yes	42
4.3	odd	2		2208.2.j.d.47.27		42
8.3	odd	2		552.2.j.c.323.29	✓	42
8.5	even	2		2208.2.j.c.47.27		42
12.11	even	2		2208.2.j.c.47.28		42
24.5	odd	2		2208.2.j.d.47.28		42
24.11	even	2	inner	552.2.j.d.323.14	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.j.c.323.29	✓	42	8.3	odd	2
552.2.j.c.323.30	yes	42	3.2	odd	2
552.2.j.d.323.13	yes	42	1.1	even	1	trivial
552.2.j.d.323.14	yes	42	24.11	even	2	inner
2208.2.j.c.47.27		42	8.5	even	2
2208.2.j.c.47.28		42	12.11	even	2
2208.2.j.d.47.27		42	4.3	odd	2
2208.2.j.d.47.28		42	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.964429 - 1.03435i) q^{2} +(-0.513686 + 1.65412i) q^{3} +(-0.139754 + 1.99511i) q^{4} +2.51134 q^{5} +(2.20635 - 1.06396i) q^{6} -2.77384i q^{7} +(2.19842 - 1.77959i) q^{8} +(-2.47225 - 1.69940i) q^{9} +O(q^{10})\)	\(q+(-0.964429 - 1.03435i) q^{2} +(-0.513686 + 1.65412i) q^{3} +(-0.139754 + 1.99511i) q^{4} +2.51134 q^{5} +(2.20635 - 1.06396i) q^{6} -2.77384i q^{7} +(2.19842 - 1.77959i) q^{8} +(-2.47225 - 1.69940i) q^{9} +(-2.42201 - 2.59760i) q^{10} -5.36177i q^{11} +(-3.22837 - 1.25603i) q^{12} +3.90363i q^{13} +(-2.86912 + 2.67518i) q^{14} +(-1.29004 + 4.15406i) q^{15} +(-3.96094 - 0.557650i) q^{16} -6.27537i q^{17} +(0.626542 + 4.19612i) q^{18} -0.842460 q^{19} +(-0.350970 + 5.01040i) q^{20} +(4.58828 + 1.42488i) q^{21} +(-5.54594 + 5.17105i) q^{22} +1.00000 q^{23} +(1.81436 + 4.55061i) q^{24} +1.30682 q^{25} +(4.03772 - 3.76478i) q^{26} +(4.08098 - 3.21646i) q^{27} +(5.53413 + 0.387656i) q^{28} +4.73312 q^{29} +(5.54090 - 2.67195i) q^{30} -5.16790i q^{31} +(3.24324 + 4.63480i) q^{32} +(8.86904 + 2.75427i) q^{33} +(-6.49092 + 6.05215i) q^{34} -6.96606i q^{35} +(3.73600 - 4.69492i) q^{36} -5.17881i q^{37} +(0.812493 + 0.871397i) q^{38} +(-6.45709 - 2.00524i) q^{39} +(5.52098 - 4.46915i) q^{40} +8.80915i q^{41} +(-2.95125 - 6.12008i) q^{42} +0.848253 q^{43} +(10.6973 + 0.749330i) q^{44} +(-6.20867 - 4.26777i) q^{45} +(-0.964429 - 1.03435i) q^{46} -4.84556 q^{47} +(2.95710 - 6.26543i) q^{48} -0.694215 q^{49} +(-1.26033 - 1.35171i) q^{50} +(10.3802 + 3.22357i) q^{51} +(-7.78818 - 0.545549i) q^{52} +11.2894 q^{53} +(-7.26275 - 1.11911i) q^{54} -13.4652i q^{55} +(-4.93630 - 6.09809i) q^{56} +(0.432759 - 1.39353i) q^{57} +(-4.56476 - 4.89570i) q^{58} -12.0771i q^{59} +(-8.10753 - 3.15432i) q^{60} +10.9153i q^{61} +(-5.34541 + 4.98407i) q^{62} +(-4.71387 + 6.85765i) q^{63} +(1.66613 - 7.82458i) q^{64} +9.80334i q^{65} +(-5.70469 - 11.8300i) q^{66} -1.54517 q^{67} +(12.5201 + 0.877009i) q^{68} +(-0.513686 + 1.65412i) q^{69} +(-7.20534 + 6.71827i) q^{70} +1.08766 q^{71} +(-8.45929 + 0.663596i) q^{72} -1.99252 q^{73} +(-5.35669 + 4.99459i) q^{74} +(-0.671293 + 2.16164i) q^{75} +(0.117737 - 1.68080i) q^{76} -14.8727 q^{77} +(4.15329 + 8.61280i) q^{78} +9.76669i q^{79} +(-9.94725 - 1.40045i) q^{80} +(3.22408 + 8.40270i) q^{81} +(9.11173 - 8.49580i) q^{82} -9.45161i q^{83} +(-3.48403 + 8.95500i) q^{84} -15.7596i q^{85} +(-0.818080 - 0.877389i) q^{86} +(-2.43134 + 7.82917i) q^{87} +(-9.54175 - 11.7874i) q^{88} +11.4954i q^{89} +(1.57346 + 10.5379i) q^{90} +10.8281 q^{91} +(-0.139754 + 1.99511i) q^{92} +(8.54835 + 2.65468i) q^{93} +(4.67319 + 5.01199i) q^{94} -2.11570 q^{95} +(-9.33255 + 2.98389i) q^{96} +9.24065 q^{97} +(0.669521 + 0.718060i) q^{98} +(-9.11179 + 13.2557i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) \) 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9	\( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24} + 22 q^{25} + 11 q^{26} - 16 q^{27} + 6 q^{28} + 2 q^{30} - 20 q^{32} + 12 q^{33} + 14 q^{34} - 24 q^{36} - 22 q^{38} + 8 q^{39} + 4 q^{40} - 44 q^{42} + 28 q^{43} + 56 q^{44} - 8 q^{45} + 30 q^{48} - 50 q^{49} + 20 q^{50} + 28 q^{51} - q^{52} + 24 q^{53} + 52 q^{54} - 34 q^{56} - 8 q^{57} - 21 q^{58} - 42 q^{60} - 79 q^{62} - 16 q^{63} + 7 q^{64} - 62 q^{66} - 4 q^{67} + 20 q^{68} + 2 q^{69} - 8 q^{70} + 22 q^{72} + 4 q^{73} + 36 q^{74} - 6 q^{75} + 14 q^{76} + 32 q^{77} + 27 q^{78} - 52 q^{80} + 18 q^{81} + 11 q^{82} - 80 q^{84} - 28 q^{86} - 48 q^{87} - 38 q^{88} - 46 q^{90} - 8 q^{91} + 4 q^{92} - 22 q^{93} + q^{94} - 16 q^{95} + 9 q^{96} + 20 q^{97} + 64 q^{98}+O(q^{100}) \) 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * q^96 + 20 * q^97 + 64 * q^98

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